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Example 8.88 from Elementary Algebra, 8.9 Use Direct and Inverse Variation
Use Direct and Inverse Variation: example 8.88
The number of gallons of gas Eunice’s car uses varies directly with the number of miles she drives. Last week she drove 469.8 miles and used 14.5 gallons of gas.
- ⓐ Write the equation that relates the number of gallons of gas used to the number of miles driven.
- ⓑ How many gallons of gas would Eunice’s car use if she drove 1000 miles?
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
The number of gallons of gas varies directly with the number of miles driven. First we will name the variables. Let number of gallons of gas.
number of miles drivenWrite the formula for direct variation. We will use in place of and in place of . Substitute the given values for the variables. Solve for the constant of variation. We will round to the nearest thousandth. Write the equation that relates and . Substitute in the constant of variation.
ⓑ
Notice that in this example, the units on the constant of variation are gallons/mile. In everyday life, we usually talk about miles/gallon.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
The distance that Brad travels varies directly with the time spent traveling. Brad travelled 660 miles in 12 hours,
- ⓐ Write the equation that relates the number of miles travelled to the time.
- ⓑ How many miles could Brad travel in 4 hours?
How did it go?