Algebra Word Problems Practice Questions Set 1

Algebra Word Problems

Basic algebra problems ask you to solve equations in which one or more elements are unknown. The unknown quantities are represented by variables, which are letters of the alphabet, such as x or y. The questions in this set of practice problems give you practice in writing algebraic equations and using these expressions to solve problems.

Assume that the number of hours Katie spent practicing soccer is represented by x. Michael practiced 4 hours less than 2 times the number of hours that Katie practiced. How long did Michael practice?
1. 2x – 4
2. 2x + 4
3. 2x + 8
4. 4x + 4
Patrick gets paid three dollars less than four times what Kevin gets paid. If the number of dollars that Kevin gets paid is represented by x, what does Patrick get paid?
1. 3 – 4x
2. 3x – 4
3. 4x – 3
4. 4 – 3x
If the expression 9y – 5 represents a certain number, which of the following could NOT be the translation?
1. five less than nine times y
2. five less than the sum of 9 and y
3. the difference between 9y and 5
4. the product of nine and y, decreased by 5
Susan starts work at 4:00 and Dee starts at 5:00. They both finish at the same time. If Susan works x hours, how many hours does Dee work?
1. x + 1
2. x – 1
3. x
4. 2x
Frederick bought 11 books that cost d dollars each. What is the total cost of the books?
1. d + 11
2. d – 11
3. 11d
There are m months in a year, w weeks in a month and d days in a week. How many days are there in a year?
1. mwd
2. m + w + d
Carlie received x dollars each hour she spent babysitting. She babysat a total of h hours. She then gave half of the money to a friend who had stopped by to help her. How much money did Carlie have after she had paid her friend?
2. + h
3. + x
4. 2hx
A long distance call costs x cents for the first minute and y cents for each additional minute. How much would a 10-minute call cost?
1. 10xy
2. x + 10y
4. x + 9y
Melissa is four times as old as Jim. Pat is 5 years older than Melissa. If Jim is y years old, how old is Pat?
1. 4y + 5
2. 5y + 4
3. 4 × 5y
4. y + 5
Sally gets paid x dollars per hour for a 40-hour work week and y dollars for each hour she works over 40 hours. How much did Sally earn if she worked 48 hours?
1. 48xy
2. 40y + 8x
3. 40x + 8y
4. 48x + 48y
Eduardo is combining two 6-inch pieces of wood with a piece that measures 4 inches. How many total inches of wood does he have?
1. 10 inches
2. 16 inches
3. 8 inches
4. 12 inches
Mary has $2 in her pocket. She does yard work for four different neighbors and earns $3 per yard. She then spends $2 on a soda. How much money does she have left?
1. $18
2. $10
3. $12
4. $14
Ten is decreased by four times the quantity of eight minus three. One is then added to that result. What is the final answer?
1. –5
2. –9
3. 31
4. –8
The area of a square whose side measures four units is added to the difference of eleven and nine divided by two. What is the total value?
1. 9
2. 16
3. 5
4. 17
Four is added to the quantity three minus the sum of negative seven and six. This answer is then multiplied by three. What is the result?
1. 30
2. –21
3. 36
4. 57
John and Charlie have a total of 80 dollars. John has x dollars. How much money does Charlie have?
1. 80
2. 80 + x
3. 80 – x
4. x – 80
The temperature in Hillsville was 20° Celsius. What is the equivalent of this temperature in degrees Fahrenheit?
1. 4°
2. 43.1°
3. 68°
4. 132°
Peggy's town has an average temperature of 23° Fahrenheit in the winter. What is the average temperature on the Celsius scale?
1. –16.2°
2. 16.2°
3. 5°
4. –5°
Celine deposited $505 into her savings account. If the interest rate of the account is 5% per year, how much interest will she have made after 4 years?
1. $252.50
2. $606
3. $10,100
4. $101
A certain bank pays 3.4% interest per year for a certificate of deposit, or CD. What is the total balance of an account after 18 months with an initial deposit of $1,250?
1. $765
2. $2,015
3. $63.75
4. $1,313.75

Answers

The following explanations show one way in which each problem can be solved. You may have another method for solving these problems.

a. The translation of "two times the number of hours" is 2x. Four hours less than 2x becomes 2x – 4.
c. When the key words less than appear in a sentence, it means that you will subtract from the next part of the sentence, so it will appear at the end of the expression. "Four times a number" is equal to 4x in this problem. Three less than 4x is 4x – 3.
b. Each one of the answer choices would translate to 9y – 5 except for choice b. The word sum is a key word for addition, and 9y means "9 times y."
b. Since Susan started 1 hour before Dee, Dee has been working for one less hour than Susan had been working. Thus, x – 1.
c. Frederick would multiply the number of books, 11, by how much each one costs, d. For example, if each one of the books cost $10, he would multiply 11 times $10 and get $110. Therefore, the answer is 11d.
a. In this problem, multiply d and w to get the total days in one month and then multiply that result by m, to get the total days in the year. This can be expressed as mwd, which means m times w times d.
a. To calculate the total she received, multiply x dollars per hour times h, the number of hours she worked. This becomes xh. Divide this amount by 2 since she gave half to her friend. Thus, is how much money she has left.
d. The cost of the call is x cents plus y times the additional minutes. Since the call is 10 minutes long, she will pay x cents for 1 minute and y cents for the other nine. Therefore the expression is 1x + 9y, or x + 9y, since it is not necessary to write a 1 in front of a variable.
a. Start with Jim's age, y, since he appears to be the youngest. Melissa is four times as old as he is, so her age is 4y. Pat is 5 years older than Melissa, so Pat's age would be Melissa's age, 4y, plus another 5 years. Thus, 4y + 5.
c. Since she worked 48 hours, Sally will get paid her regular amount, x dollars, for 40 hours and a different amount, y, for the additional 8 hours. This becomes 40 times x plus 8 times y, which translates to 40x + 8y.
b. This problem translates to the expression 6 × 2 + 4. Using order of operations, do the multiplication first; 6 × 2 = 12 and then add 12 + 4 = 16 inches.
c. This translates to the expression 2 + 3 × 4 – 2. Using order of operations, multiply 3 × 4 first; 2 + 12 – 2. Add and subtract the numbers in order from left to right; 2 + 12 = 14; 14 – 2 = 12.
b. This problem translates to the expression 10 – 4 (8 – 3) + 1. Using order of operations, do the operation inside the parentheses first; 10 – 4 (5) + 1. Since multiplication is next, multiply 4 × 5; 10 – 20 + 1. Add and subtract in order from left to right; 10 – 20 = –10; –10 + 1 = –9.
d. This problem translates to the expression 4² + (11 – 9) ÷ 2. Using order of operations, do the operation inside the parentheses first; 4² + (2) ÷ 2. Evaluate the exponent; 16 + (2) ÷ 2. Divide 2 ÷ 2; 16 + 1. Add; 16 + 1 = 17.
c. This problem translates to the expression 3 {[3 – (–7 + 6)] + 8}. When dealing with multiple grouping symbols, start from the innermost set and work your way out. Add and subtract in order from left to right inside the brackets. Remember that subtraction is the same as adding the opposite so 3 – (–1) becomes 3 + (+1) = 4; 3 {[3 – (–1)] + 8]}; 3 [4 + 8]. Multiply 3 × 12 to finish the problem; 3 [12] = 36.
c. If the total amount for both is 80, then the amount for one person is 80 minus the amount of the other person. Since John has x dollars, Charlie's amount is 80 – x.
c. Use the formula F = C + 32. Substitute the Celsius temperature of 20° for C in the formula. This results in the equation F = (20) + 32. Following the order of operations, multiply and 20 to get 36. The final step is to add 36 + 32 for an answer of 68°.
d. Use the formula C = (F – 32). Substitute the Fahrenheit temperature of 23° for F in the formula. This results in the equation C = (23 – 32). Following the order of operations, begin calculations inside the parentheses first and subtract 23 – 32 to get –9. Multiply times –9 to get an answer of –5°.
d. Using the simple interest formula Interest = principal × rate × time, or I = prt, substitute p = $505, r = .05 (the interest rate as a decimal) and t = 4; I = (505)(.05)(4). Multiply to get a result of I = $101.
d. Using the simple interest formula Interest = principal × rate × time, or I = prt, substitute p = $1,250, r = 0.034 (the interest rate as a decimal), and t = 1.5 (18 months is equal to 1.5 years); I = (1,250)(.034)(1.5). Multiply to get a result of I = $63.75. To find the total amount in the account after 18 months, add the interest to the initial principal. $63.75 + $1,250 = $1,313.75.

More practice problems on algebra word problems can be found at:

Algebra Word Problems Practice Questions Set 1 (You are here)
Algebra Word Problems Practice Questions Set 2
Algebra Word Problems Practice Questions Set 3
Algebra Word Problems Practice Questions Set 4
Algebra Word Problems Practice Questions Set 5
Algebra Word Problems Practice Questions Set 6

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