Question

During a 60-minute period, a traffic engineer counted 66 trucks and cars that crossed a bridge. The ratio of trucks to cars that travel across the bridge is usually 3:8. The equation 3 8 = t 66 − t 3 8 = t 66 − t can be used to predict the number of trucks, t, the engineer should have counted. How many trucks should the engineer have counted?

Answer 1

18

Explanation:

t = Number of trucks counted

c = Number of cars

Ratio of trucks to cars =
`(t)/(c)=(3)/(8)`

Total number of cars and truck = 66

`t+c=66`

Divide the left and right side by the number of cars

`(t+c)/(c)=(66)/(c)\\\Rightarrow (t)/(c)+1=(66)/(c)\\\Rightarrow (3)/(8)+1=(66)/(c)\\\Rightarrow (11)/(8)=(66)/(c)\\\Rightarrow c=66* (8)/(11)\\\Rightarrow c=48`

Total number of cars is 48

so

`t=66-c\\\Rightarrow t=66-48\\\Rightarrow t=18`

Total number of trucks counted is 18.