Question

Trace is filling up a small pool for his little cousin. He notices that 1/3 of a barrel of water fills up 5/7 of the pool. What fraction of a barrel is needed to fill the entire pool?

a. 2/15
b. 5/21
c. 7/15
d. 5/3

Answer 1

To fill the entire pool, Trace needs 7/15 of a barrel of water, as determined by setting up a proportion based on the given relationship between the fraction of a barrel used and the portion of the pool filled. The correct choice is c. 7/15.

Step-by-step explanation:

To find the fraction of a barrel needed to fill the entire pool, we start by understanding the relationship between the amount of water and the pool's capacity. Given that 1/3 of a barrel fills 5/7 of the pool, we can set up a proportion to find the total fraction needed to fill the pool completely. We assume that the fraction of the barrel needed to fill the pool is X, so the proportion would be:

1/3 : 5/7 = X : 1

To solve for X, we can cross-multiply and divide:

(1/3) * 1 = (5/7) * X

To isolate X, we multiply both sides by 7/5:

X = (1/3) * (7/5)

Now we multiply the numerators and the denominators:

X = (1*7) / (3*5)

X = 7/15

So Trace would need 7/15 of a barrel to fill the pool completely. Therefore, the correct answer is c. 7/15.