John filled 3/8 of a tank with 3 identical jugs of water. He poured another 2 identical jugs and 9 identical cups of water to fill the tank to its brim.

Question

(a) What fraction of the tank can 1 jug of water fill?
(b) If only cups are used to fill the empty tank to its brim, how many
identical cups are needed?

Answer 1

3 identical jugs can fill 3/8 pour of a tank.
fraction of the tank filled by one jug = 3/8 / 3 = 1/8
Total number of jugs required = 3 + 2 = 5
Parts filled = 5/8
Remaining part = 1/1 - 5/8 = 3/8
9 cup fill 3/8 part
1 cup will fill, 3/8 / 9 pour
= 1/24
So, no. of cup required to fill the entire tank = 1 / 1/24 = 1 * 24 = 24

(a) 1/8 (b) 24

Answer 2

let capacity of tank be t
3j = 3t/8
j = t/8 ----> one jug fills 1/8 of the tank
t = 8j

2j + 9c = t

2j + 9c = 8j
9c = 6j = 6(t/8) = (3/4)t
36/3 = t
t = 12
it would take 12 cups to fill the tank