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

Answer:

18

Step-by-step explanation:

t = Number of trucks counted

c = Number of cars

Ratio of trucks to cars = $\dfrac{t}{c}=\dfrac{3}{8}$

Total number of cars and truck = 66

$t+c=66$

Divide the left and right side by the number of cars

$\dfrac{t+c}{c}=\dfrac{66}{c}\\\Rightarrow \dfrac{t}{c}+1=\dfrac{66}{c}\\\Rightarrow \dfrac{3}{8}+1=\dfrac{66}{c}\\\Rightarrow \dfrac{11}{8}=\dfrac{66}{c}\\\Rightarrow c=66\times \dfrac{8}{11}\\\Rightarrow c=48$

Total number of cars is 48

so

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

Total number of trucks counted is 18.