The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

Complete Question:

The only types of vehicles sold at a certain dealership last month were sedans, trucks, and vans. If the ratio of the number of sedans to the number of trucks to the number of vans sold at the dealership last month was 4:5:7, respectively, what was the total number of vehicles sold at the dealership last month?

1) The number of vans sold at the dealership last month was between 10 and 20.

2) The number of sedans sold at the dealership last month was less than 10.

The total number of vehicles sold = 32

Step-by-step explanation:

Since the ratio of sales is 4:5:7

Let m be a common factor

The number of sedans sold = 4m

The number of trucks sold = 5m

The number of vans sold = 7m

In (1)

Since the number of vans sold was between 10 and 20. i.e 10 ≤ 7m ≤20

The only multiple of 7 between 10 and 20 is 14

Therefore, 7m = 14; m=2

in (2)

The number of sedans sold was less than 10 i.e. 0 < 4m < 10

There are two multiples of 4 between 0 and 10, they are 4 and 8

for 4m = 4; m=1

for 4m = 8; m=2

m = 2 is the only consistent value in (1) and (2)

The number of sedans sold = 4m = 4 *2 = 8

The number of trucks sold = 5m = 5 * 2 = 10

The number of vans sold = 7m = 7*2 = 14

The total number of vehicles sold = 8 + 10 + 14

The total number of vehicles sold = 32

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step-by-step explanation: