Question

There are 2820 cars in Farmington. The ratio of medium size cars to compacts is 7 to 5 and the ratio of compacts to full-size cars is 8 to 9.How many full-size cars are there?

Answer 1

Answer:

Number of full size cars = 900

Step-by-step explanation:

The ratio of medium size cars to compacts is 7 to 5 and the ratio of compacts to full-size cars is 8 to 9. Since compact cars are  there in both ratios , we need to  make the number in the ratio for compact cars to be the same.

$\frac{medium}{compact} = \frac{7}{5}$

Multiply by 8 on numerator and denominator

$\frac{medium}{compact} = \frac{56}{40}$

$\frac{compact}{full size} = \frac{8}{9}$

Multiply numerator and denominator by 5.

$\frac{compact}{full size} = \frac{40}{45}$

Ratio of medium, compact and full size are in ratio 56,40,45.

Total number of cars =2820.

(56 + 40 + 45)x = 2820

x = $\frac{2820}{141}$

x = 20

Number of full size cars = $20\times 45$ =900