Question

During a 60-minute period, a traffic engineer counted 54 trucks and cars that crossed a bridge. The ratio of trucks to cars that travel across the bridge is usually 2:7. The equation LaTeX: \frac{2}{7}=\frac{t}{54-t}2 7 = t 54 − 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

The engineer should have counted 12 trucks.

Step-by-step explanation:

To find the number of trucks the engineer should have counted, we can solve the given equation:
2/7 = t/(54-t)

Multiplying both sides of the equation by (54 - t) gives us:

(2/7)(54 - t) = t

Expanding the equation:

108/7 - (2/7)t = t

Adding (2/7)t to both sides:

108/7 = (9/7)t

Multiplying both sides by 7/9:

12 = t

Therefore, the engineer should have counted 12 trucks.