If you know how to write linear equations and evaluate them, you'll be able to solve a wide range of algebra word problems on the GRE Mathematical Reasoning test.

Many of the questions on the test challenge your ability to find the value of an unknown variable using known values presented in the question. The following problems ask you to calculate how many chocolate bars you can buy with a given amount of money, allowing for sales tax, and to figure out how many hours two people worked, given the total amount paid, and the fact that they received different pay rates.

## Practice questions

If you have $10 in your pocket and you're craving a candy bar priced at $0.88 with 7 percent sales tax, how many candy bars can you afford to purchase?

Gilbert and Sullivan paint houses. Gilbert is faster, so he earns $15.00 an hour, while Sullivan earns only $10.00 an hour. They work the same number of hours painting a house and are paid $1,500. How many hours did they work?

## Answers and explanations

10 candy bars

The unknown is the number of candy bars,

*c,*and the maximum amount you can spend is $10, so place*c*on one side and $10 on the other. The total price you'll pay for the candy bars before tax is $0.88 per candy bar times the number of candy bars, or $0.88*c.*You also need to add in the 7 percent sales tax on those candy bars, so your expression ends up looking like this:To isolate the variable, first multiply $0.88

*c*by 0.07, and you get $0.0616*c,*which is the amount of sales tax you'll pay. Then add $0.0616*c*to $0.88*c*and you get $0.9416*c.*Divide both sides by $0.9416 and you get*c*= 10.62. Of course, you can't buy 0.62 candy bars, so the most candy bars you could buy is 10.60 hours

Let

*h*be the number of hours Gilbert and Sullivan worked. Gilbert earned $15.00*h,*and Sullivan earned $10.00*h,*for a total of $1,500. Create your equation and solve for*h:*