# Ratios, Rates, and Proportions

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## 5/12 Ratios, Rates, and Proportions

The c cars in a car service use a total of g gallons of gasoline per week. If each of the cars uses the same amount of gasoline, then, at this rate, which of the following represents the number of gallons used by 5 of the cars in 2 weeks?

First, note the bottom line.

5 cars 2 weeks = ?

Next, assess your options. Since the problem gives so much information about the cars using words rather than numbers, a good place to start is to translate its question into mathematical terms.

c = total number of cars

g = total gallons of gas per week

The gas used in two weeks is easy to find: 2g. The tricky part involves determining how much gas is used by only 5 cars. It is tricky rather than difficult because if you know the trick, this problem is easy. Simply find the gas used by one car over the course of a week and multiply that by 5 cars.

$\frac{g}{c}$ = gas per week for 1 car

$\frac{5g}{c}$ = gas per week for 5 cars

Since the question asks how much gas will be used in 2 weeks, multiply this term by 2. This incorporates the 2g you identified earlier.

$\frac{10g}{c}$ = gas for 5 cars for 2 weeks

Now look at the answer choices.

A) $10cg$

B) $\frac{2g}{5c}$

C) $\frac{5g}{2c}$

D) $\frac{g}{10c}$

E) $\frac{10g}{c}$