Math Word Problems Practice Quiz (page 2)
Math Word Problems Practice Quiz
This test has 30 multiple-choice questions and is in the same format as the introductory test (Introductory Math Word Problems Practice Quiz). Each question corresponds with the concepts studied in the lesson in this book with the same number. Take the test to identify your areas of improvement. You may also use the test to help indicate areas where there is room for some growth in the skills and strategies needed for solving math word problems.
Read and answer each problem carefully by selecting the best answer choice. Don't be afraid to show your work; it is the cornerstone of problem solving and will also help you to identify any mistakes. When you have completed the test, check your responses with the answer key at the end of the section. Each answer explanation uses the same format used for word-problem solving throughout the book. Use these steps to help create your plan for word-problem solving success.
- Which statement means the same as "four more than five times a number, n"?
- 5n + 4
- 4n + 5
- n + 4
- Sarevah's team is playing in a soccer tournament. During the tournament, each team will play each of the other teams exactly once. If there are 5 teams in the tournament, what is the total number of games that will be layed during the tournament?
- 5 games
- 10 games
- 15 games
- 25 games
- Teresa has 6 more pencils in her case than Ken. Becky has twice as many pencils as Teresa. If Ken has 12 pencils, how many does Becky have?
- 12 pencils
- 18 pencils
- 24 pencils
- 36 pencils
- Kevin needs a ride and decides to take a taxicab. If it costs $6.50 to ride 4 miles in the cab, then what is the total amount it would cost to ride 16 miles at the same rate?
- Sherry has a bank that contains only quarters and dimes. There is a total of $2.40 in the bank. What is the greatest number of quarters that she could have in her bank?
- 7 quarters
- 8 quarters
- 9 quarters
- 10 quarters
- Todd is thinking of a number. His number is equal to two times the sum of 16 and 4. What is his number?
- A DVD player is on sale for of the original price. If the original price was $69, what is the sale price of the player?
- At a hot dog stand, Steve spent $18 on hot dogs for his family. If he bought a total of 8 hot dogs, how much did each one cost?
- The sale price for 4 pounds of bananas is $1.32. What is the cost for 1 pound of bananas?
- If 5 pounds of apples cost $8.45, what is the cost of 7 pounds?
- Fifteen is what percent of 60?
- On a science quiz, Peter received a 90%. If he answered 36 questions correctly and each question is worth the same number of points, what was the total number of questions on the test?
- 32 questions
- 38 questions
- 40 questions
- 46 questions
- The product of 6 and a number increased by 10 is equal to 8 times the number. What is the number?
- Joe wants to run at least 18 miles this week. If he runs 3 miles on Monday and twice as many miles on Wednesday, what is the minimum number of miles he still has to run this week to reach his goal?
- 6 miles
- 9 miles
- 12 miles
- 18 miles
- The distance from Earth to the sun is approximately 150,000,000 kilometers (km). What is this distance in scientific notation?
- 1.5 × 107 km
- 15.0 × 108 km
- 1.5 × 108 km
- 15 × 108 km
- Toby mixes coffee that costs $5 per pound with coffee that costs $7.50 per pound. He buys 4 more pounds of the coffee that costs $7.50 per pound than the coffee that costs $5 per pound. If he spends a total of $55 on coffee, how many pounds of coffee did he buy in all?
- 2 pounds
- 4 pounds
- 6 pounds
- 8 pounds
- Two angles are supplementary. If the measure of one angle is 30 degrees less than the measure of the other angle, what is the measure of the smaller angle?
- 30 degrees
- 75 degrees
- 105 degrees
- 180 degrees
- The measure of one angle of a triangle is 65 degrees, and the measure of the second angle is 10 degrees more than the first. What is the measure of the third angle of the triangle?
- 40 degrees
- 50 degrees
- 65 degrees
- 75 degrees
- The measure of angle in rhombus ABCD is equal to twice the measure of angle B. What is the measure of angle ?
- 30 degrees
- 60 degrees
- 90 degrees
- 120 degrees
- The ratio of the corresponding sides of two similar triangles is 1:4. What is the ratio of their perimeters?
- The measure of two different sides of an equilateral triangle can be expressed as 2x – 1 and 4x – 11. What is the measure of the perimeter of this triangle?
- The circumference of a circle is C = 16π. How many units is the radius of this circle?
- 4 units
- 8 units
- 16 units
- 32 units
- Richard is tiling a rectangular floor with a length of 12 feet and a width of 20 feet. If each tile will cover 4 square feet, how many tiles does he need?,/li>
- 20 tiles
- 24 tiles
- 60 tiles
- 240 tiles
- A box in the shape of a cube has an edge of 3 meters. How many square meters of paper would be needed to cover the entire cube?
- 9 m2
- 27 m2
- 54 m2
- 81 m2
- A toy box in the shape of a rectangular prism has a length of 4 feet, a width of 2 feet, and a height of 1.5 feet. What is the volume of the toy box?
- 12 cubic feet
- 15.5 cubic feet
- 24 cubic feet
- 34 cubic feet
- Kevin is graphing a figure with the points (–2,1), (–3,4), and (–8,8). In what quadrant is the figure located?
- Quadrant I
- Quadrant II
- Quadrant III
- Quadrant IV
- Larry is playing a board game and needs to roll a 3 on a regular die on his next turn in order to win the game. What is the probability that Larry will win the game on his next turn?
- There are 6 black marbles and 3 red marbles in a bag. A marble is selected, not replaced, and then another is selected. What is the probability that both marbles selected are red?
- Ted has 5 different shirts and 6 pairs of pants in his closet. How many different outfits can he make by selecting one shirt and one pair of pants?
- 6 outfits
- 11 outfits
- 30 outfits
- 36 outfits
- The elevations of 5 mountains are 29,035 feet, 28,169 feet, 27,765 feet, 27,920 feet, and 28,253. What is the median elevation of these mountains?
- 1,270 feet
- 28,169 feet
- 28,228 feet
- 28,253 feet
- a. Read and understand the question. This question is asking you to translate from words into math symbols.
- b. Read and understand the question. This question is asking for the total number of games to be played in a tournament. Each of the 5 teams plays each team exactly once.
- d. Read and understand the question. This question is looking for the number of pencils Becky has. Information is also given about Ken's number of pencils and Teresa's number of pencils.
- c. Read and understand the question. Kevin's 4-mile cab ride costs $6.50. Find the total cost of going 16 miles.
Make a plan. Translate using the key words and phrases in the question. Carry out the plan. The key phrase more than means addition. The phrase "five times a number" translates to 5n. The final expression is 5n + 4.
Check your work. The only choices with five times a number written correctly are choices a and d. Choice d is not correct because 4 is being multiplied, not added.
Make a plan. Call the teams A, B, C, D, and E, and make an organized list of all of the games that will be played. Note that if Team A plays Team B, that is the same as Team B plays Team A.
Carry out the plan. The organized list could look like the following:
|A plays B||A plays C||A plays D||A plays E|
|B plays C||B plays D||B plays E|
|C plays D||C plays E|
|D plays E|
This is a total of 10 games.
Check your work. The number of games played can also be found by adding 4 + 3 + 2 + 1 = 10, which is the same solution reached with the organized list.
Make a plan. Use the problem solving strategy of working backward, and start with the fact that Ken has 12 pencils.
Carry out the plan. Since Ken has 12 pencils, and Teresa has 6 more than Ken, Teresa has 12 + 6 = 18 pencils. Because Becky has twice as many as Teresa has, Becky has 2 × 18 = 36 pencils.
Check your work. Start with 12, add 6 to get 18, and double this amount to get 36.
Make a plan. Look for a pattern using the fact that 4 miles costs $6.50,and go up 4 miles each time by adding another $6.50 until reaching 16 miles.
Carry out the plan. The pattern may look like the following:
|Number of miles||4||8||12||16|
The total cost of 16 miles is $26.00.
Check your work. Another way to solve this problem is to set up a proportion and cross multiply. The proportion could be set up as .Cross multiply to get 4x = 104. Divide each side of the equation by 4.
- x = $26
which is the same solution as the previous method.
Make a plan. Use the strategy of guess and check. Remember to look for the greatest number of quarters. When using this strategy, do at least three trials to be sure of your solution.
Carry out the plan. Since 10 quarters is equal to $2.50, try 9 quarters first. Nine quarters is equal to $2.25. There is no way to add a number of dimes to this amount to get exactly $2.40. For the second trial, try 8 quarters. Eight quarters is equal to $2.00, so add 4 dimes to this amount to get $2.40. To be sure, try 7 quarters. Seven quarters is equal to $1.75, and there is no way to add a number of dimes to this amount and get exactly $2.40. The greatest number of quarters is 8.
Check your work. Eight quarters is equal to $2.00, added to 4 dimes is equal to $2.00 + $0.40 = $2.40.
Make a plan. Find a number that is equal to 2 times the sum of 16 and 4.
Carry out the plan. First, find the sum of 16 and 4. Sum is a key word for addition, so 16 + 4 = 20. Then, find 2 times this sum: 2 × 20 = 40. His number is 40.
Check your work. 2(16 + 4) = 2(20) = 40. This answer is checking.
Make a plan. To find the sale price, find of the original price by multiplying × $69.
Carry out the plan.
The sale price is $46.
Check your work. If the sale price is of the original price, you are saving of the cost.
You would save $23. To find the sale price, subtract the discount.
- $69 – $23 = $46
which is the same sale price calculated by the other method.
Make a plan. To find the cost for one, divide the total amount of money spent by the number of hot dogs purchased.
Carry out the plan: $18 ÷ 8 = $2.25. The cost for each hot dog is $2.25.
Check your work. To check this problem, multiply the price of one hot dog by 8: $2.25 × 8 = $18.00, which is the total amount that Steve spent.
Make a plan. Divide the cost of 4 pounds by 4 to find the price for 1 pound.
Carry out the plan: $1.32 ÷ 4 = $0.33. One pound of bananas is $0.33.
Check your work. To check, multiply $0.33 by 4 to find the cost of 4 pounds. This is equal to $1.32, so this answer is checking.
Make a plan. Set up a proportion comparing the cost with the number of pounds. The proportion could be set up as follows:
Carry out the plan. Use the given values in the proportion and cross multiply.
Cross multiply: 5x = 59.15. Divide each side of the equation by 5.
- x = 11.83
The cost of 7 pounds is $11.83.
Check your work. Since the price of 5 pounds is $8.45, then the price for one pound is equal to $8.45 divided by 5. The unit price is $1.69. Multiply $1.69 by 7 to get the cost for 7 pounds. This is also equal to $11.83, so this answer is checking.
Make a plan. Set up the proportion , where 15 is the part, 60 is the whole, and x is the percent to be found.
Carry out the plan. The proportion becomes . Cross multiply to get 60x = 1,500. Divide each side of the equation by 60.
- x = 25
15 is 25% of 60.
Check your work. To check this problem, find 25% of 60 by multiplying 0.25 × 60. This is equal to 15, so this answer is checking.
Make a plan. Set up a proportion comparing the correct number of questions to the corresponding percent earned, over the total of 100%.
Carry out the plan. The proportion could be set up as
Cross multiply to get 90x = 3,600. Divide each side of the equation by 90.
- x = 40
There are 40 questions on the test.
Check your work. Set up the proportion using 40 as the total number of questions. Then, cross multiply to be sure the cross products are equal.
- 3,600 = 3,600
so the proportion is checking.
Make a plan. Use the key words and phrases in the problem to write an equation using mathematical symbols. Then, solve the equation to find the number.
Carry out the plan. Let n = the number. The first part of the statement translates to 6n + 10 and the second part translates to 8n. Set these parts equal and solve the equation 6n + 10 = 8n. Subtract 6n from each side of the equation.
- 6n – 6n + 10 = 8n – 6n
The equation becomes 10 = 2n. Divide each side of the equation by 2 to get n = 5. The number is 5.
Check your work. Substitute 5 for "the number" in the question. The product of six and five is 30, increased by 10 is 30 + 10 = 40. Eight times 5 is equal to 40. The results are equal, and the answer is checking.
Make a plan. Write an inequality that relates the miles he has run so far to the goal of 18 miles.
Carry out the plan. Let m = the minimum number of miles he still needs to run. He ran 3 miles on Monday, plus twice as many (6) on Tuesday. Add these amounts to m and set the sum greater than or equal to 18. The inequality is 3 + 6 + m ≥ 18. Combine like terms: 9 + m ≥ 18. Subtract 9 from each side: 9 – 9 + m ≥ 18 – 9. The inequality is m ≥ 9. Joe must run a minimum of 9 miles.
Check your work. Add the amounts for Monday, Tuesday, and the miles to go together: 3 + 6 + 9 = 18, which was the minimum amount. This answer is checking.
Make a plan. Write the non-zero numbers as a value between 1 and 10. Multiply this value by a power of 10, where the exponent is the number of places the decimal moves to the left. The exponent is positive since the original number is greater than 1.
Carry out the plan. Place the decimal point between 1 and 5 to create a number between 1 and 10. The exponent is 8 because the decimal point has been moved 8 places to the left. The scientific notation is 1.5 × 108.
Check your work. To check this problem, take 1.5 and move the decimal point 8 places to the right. Add zeros where needed. This makes the number 150,000,000, which was the original number. This answer is checking.
Make a plan. There are 4 more pounds of the more expensive coffee, so let x represent the less expensive coffee and x + 4 represent the more expensive coffee. Write an expression for the sum of the money spent on both types and set it equal to $55.
Carry out the plan. Let x = the number of pounds of the $5.00 coffee, and let x + 4 = the number of pounds of the $7.50 coffee. Write the equation
- $5.00(x) + $7.50(x + 4) = $55.00
Use the distributive property within the equation to get 5x + 7.5x + 30 = 55. Combine like terms to get 12.5x + 30 = 55. Subtract 30 from each side of the equation: 12.5x + 30 – 30 = 55 – 30. Simplify: 12.5x = 25. Divide each side of the equation by 12.5:
Thus, x = 2 and x + 4 = 2 + 4 = 6. Toby bought 2 pounds of the $5.00 coffee and 6 pounds of the $7.50 coffee. This is a total of 2 + 6 = 8 pounds. Check your work. Two pounds of the $5.00 per pound coffee costs 2($5) = $10. Six pounds of the $7.50 per pound coffee costs 6($7.50) = $45. The total for both types is $10 + $45 = $55, which was the total amount spent in the problem. This answer is checking.
Make a plan. The sum of two supplementary angles is 180 degrees. Use the information given about the two angles to write an equation set equal to 180.
Carry out the plan. Let x = the larger angle and let x – 30 = the smaller angle. The term supplementary means that the sum of the two angles is 180 degrees. To write the equation, add the two angles and set the sum equal to 180.
- x + x – 30 = 180
Combine like terms to get 2x – 30 = 180. Add 30 to each side of the equation.
- 2x – 30 + 30 = 180 + 30
The equation simplifies to 2x = 210. Divide each side of the equation by 2.
- x = 105
Therefore, the larger angle is 105 degrees and the smaller angle is x – 30 = 105 – 30 = 75 degrees.
Check your work. To check this problem, add the two angle measures: 105 + 75 = 180. Because the two angles are supplementary, they add to 180 degrees. This answer is checking.
Make a plan. The sum of the three angles of a triangle is 180 degrees. Use the measure of the first angle to find the measure of the second. Then, subtract the sum of these two angles from 180.
Carry out the plan. The first angle measures 65 degrees. Because the second angle is 10 degrees more than the first, the second angle measures 65 + 10 = 75 degrees. Subtract the sum of these two angles from 180: 180 – (65 + 75) = 180 – 140 = 40 degrees. The third angle is 40 degrees. Check your work. Add the measures of all three angles to be sure that they add to 180 degrees: 65 + 75 + 40 = 180. This answer is checking.
Make a plan. The measure of angle is twice the measure of angle .Write an expression for the sum of these two angles, and set the sum equal to 180 degrees to solve for the angle measures.
Carry out the plan. Angle and angle in rhombus ABCD are consecutive angles, or angles that are next to each other. Therefore, the sum of their measures is 180 degrees. Let x = the measure of angle , then 2x = the measure of angle . Because the sum of the two angles is 180 degrees, write the equation x + 2x = 180. Combine like terms: 3x = 180. Divide each side of the equation by 3.
- x = 60
Thus, the measure of angle is 60 degrees, and the measure of angle is 2(60) = 120 degrees.
Check your work. Add the measures of the consecutive angles and to be sure that the sum is 180 degrees: 60 + 120 = 180. This answer is checking.
Make a plan. Use the strategy of guess and check to try values for the sides of the triangles in the ratio of 1:4. Then, find the perimeters and compare their ratio.
Carry out the plan. Use the sides 2, 3, and 4 for the smaller triangle. Since the ratio of corresponding sides is 1:4, multiply each of these values by 4 to find the sides of the larger triangle. Therefore, the sides would be 8, 12, and 16. Now, add the sides of each triangle to find the perimeters. The smaller triangle has a perimeter of 2 + 3 + 4 = 9, and the larger triangle has a perimeter of 8 + 12 + 16 = 36. Because the ratio of 9:36 simplifies to 1:4, the ratio of their perimeters is 1:4. This is the same as the ratio of the corresponding sides.
Check your work. To check this solution, divide each of the perimeters by 9: 9 ÷ 9 = 1 and 36 ÷ 9 = 4. This is the ratio 1:4. The answer is checking.
Make a plan. Because all sides of an equilateral triangle are the same measure, set the two given expressions equal to each other and solve for x. Use this value of x to substitute and find the perimeter.
Carry out the plan. Set the two known expressions equal to each other: 2x – 1 = 4x – 11. Subtract 2x from each side of the equation:
- 2x – 2x – 1 = 4x – 2x – 11
The equation simplifies to –1 = 2x – 11. Add 11 to each side to get 10 = 2x. Divide each side of the equation by 2 to get x = 5. Substitute this value into one of the expressions to find the length of one side: 2x – 1 = 2(5) – 1 = 10 – 1 = 9. If one side is 9, then the perimeter is 3 × 9 = 27.
Check your work. Substitute the value of x into the other expression to be sure each side is 9.
- 4x – 11 = 4(5) – 11 = 20 – 11 = 9
The answer is checking.
Make a plan. Use the formula for circumference and the strategy of working backward to find the radius. The formula for the circumference of a circle is C = πd, where d is the diameter of the circle.
Carry out the plan. Because C = πd and you are given C = 16π, then the diameter (d) is equal to 16. The radius of a circle is equal to half of the diameter, and half of 16 is 8. The radius is 8 units.
Check your work. Work forward through the problem to check. If the radius is 8 units, then the diameter is 8 × 2 = 16. Thus, the circumference of this circle is C = πd = 16π. This solution is checking.
Make a plan. Find the area of the floor by using the formula Area = base × height. Then, divide this area by the area covered by each tile.
Carry out the plan. Area = 12 × 20 = 240 square feet. Divide this area by 4 to find the number of tiles needed: 240 ÷ 4 = 60. He will need 60 tiles.
Check your work. Work backward to check this problem: 60 tiles will cover 60 × 4 = 240 square feet. Because the area of the rectangular floor is also 12 × 20 = 240 square feet, this is the correct number of tiles. This solution is checking.
Make a plan. Use the formula for surface area of a cube (SA = 6e2, where e is the length of an edge of the cube). Substitute the length of the edge (3 meters) given into the formula.
Carry out the plan. The formula becomes SA = 6(3)2. Evaluate the exponent first: SA = 6(9). Multiply: SA = 54 m2.
Check your work. Work backward to check the solution. Begin with the surface area of 54 square meters. Divide this number by 6 faces:
54 ÷ 6 = 9. This is the area of each face of the cube. Because 3 × 3 = 9, each edge measures 3 meters. This solution is checking.
Make a plan. Use the volume formula V = l × w × h, and substitute the values given in the question.
Carry out the plan. The volume formula becomes V = 4 × 2 × 1.5, so V = 12. The volume is 12 cubic units.
Check your work. Double-check your work by multiplying the values to be sure the correct volume is 12 cubic units: 4 × 2 × 1.5 = 12. The answer is checking.
Make a plan. Examine the coordinates for each point, and graph each point starting at the origin. If the first number (x-coordinate) is positive, go to the right, and if the number is negative, count to the left. If the second number (y-coordinate) is positive, count up, and if it is negative, count down.
Carry out the plan. Each of the points has a negative x-coordinate and a positive y-coordinate. Each of the points should be graphed by counting over to the left and then up. The figure is a triangle located in Quadrant II, as shown in the following figure.
Check your work. Each of the points is located in the second quadrant, where x-coordinates are negative and y-coordinates are positive. This solution is checking.
Make a plan. The probability of an event e is equal to
There are 6 sides to the die, so there are 6 total outcomes. There is only one way to roll a 3.
Carry out the plan. The probability is P(E) = .
Check your work. There is only one way to roll a 3 on a 6-sided die. This makes the probability equal to . The answer is ng.
Make a plan. Use the fact that there are 3 red marbles and that there are a total of 9 marbles. Because the first marble is not replaced after it is chosen, the number of marbles decreases by one for the second draw. Find the probability of each event, and multiply them together.
Carry out the plan. The probability of first selecting a red marble at random is , which leaves only 8 marbles left. The probability of selecting another red marble second is . Multiply these probabilities to find the probability that both events will happen:
Check your answer. To check this solution, multiply the probabilities together again. Because , this answer is checking.
Make a plan. One way to solve this problem is to multiply the number of choices for each to find the total number of outfits.
Carry out the plan. Multiply 5 shirts by 6 pairs of pants: 5 × 6 = 30 different outfits.
Check your work. You can check your work by making an organized list of each shirt with each of the different pairs of pants. There are 30 different outfits in the list. This answer is checking.
Make a plan. The median elevation will be the value in the middle of the list, when the list is in order from smallest to largest. Put the values in order, and locate the middle value.
Carry out the plan. The order of the given elevations from smallest to largest is 27,765; 27,920; 28,169; 28,253, 29,035. The value in the middle of the list is 28,169 feet.
Check your work. You could also find the solution by listing the elevations in order from largest to smallest: 28,169 is the middle number in this list also. The answer is checking.
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