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Algebraic Expressions and Word Problems Practice Questions

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Updated on Oct 3, 2011

Review these concepts at Algebraic Expressions and Word Problems Study Guide.

Algebraic Expressions and Word Problems Practice Questions

Practice

1. Ben walked 20 miles in 4 hours. What was his average speed?
2. Jim and Bryan can shovel the driveway together in 6 hours. If it takes Jim 10 hours working alone, how long will it take Bryan working alone?
3. The sixth-grade class bought two different types of candy to sell at a school fund-raiser. They purchased 50 pounds of candy at \$2.25 per pound and x pounds at \$1.90 per pound. What is the total number of pounds they bought if the total amount of money spent on candy was \$169.50?

Solutions

1. Use the distance formula and substitute in the known values:

rt = d

t = 4

d = 20

r × 4 = 20

Now, isolate the variable to find the speed:

(r × 4) ÷ 4 = 20 ÷ 4

r = 5

Ben walked at a rate of 5 miles per hour.

2. Let x = the number of hours Bryan takes to shovel the driveway by himself. In 1 hour, Bryan can do of the work and Jim can do of the work. As an equation this looks like , where represents what part they can shovel in 1 hour together. Multiply both sides of the equation by the least common denominator, 30x, to get an equation of 30 + 3x = 5x. Subtract 3x from both sides of the equation: 30 + 3x – 3x = 5x – 3x. This simplifies to 30 = 2x. Divide both sides of the equal sign by 2 to get a solution of 15 hours.
3. Let x = the amount of candy at \$1.90 per pound. Let y = the total number of pounds of candy purchased. If there are also 50 pounds of candy at \$2.25 per pound, then the total amount of candy can be expressed as y = x + 50. Use the equation 1.90x + 2.25(50) = \$169.50 because the total amount of money spent was \$169.50. Multiply on the left side: 1.90x + 112.50 = 169.50. Subtract 112.50 from both sides: 1.90x + 112.50 – 112.50 = 169.50 – 112.50. Divide both sides by 1.90: . So, x = 30 pounds, which is the amount of candy that costs \$1.90 per pound. The total amount of candy is 30 + 50, which is 80 pounds.

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