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.
(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?
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
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
To solve this problem, we need to find the fraction of the tank that each jug of water fills and determine the number of cups needed to fill the tank.
(a) To find the fraction of the tank that 1 jug of water can fill, we need to determine the total number of identical jugs and cups that were used to fill the tank.
John initially filled 3/8 of the tank with 3 identical jugs of water. Each jug filled 3/8 รท 3 = 1/8 of the tank. Therefore, 1 jug of water can fill 1/8 of the tank.
(b) To find the number of identical cups needed to fill the tank, we need to determine the remaining fraction of the tank that needs to be filled after pouring the jugs.
The initial filling of 3 identical jugs filled 3/8 of the tank. To fill the tank to its brim, the remaining fraction is 1 - 3/8 = 5/8.
Now, John poured another 2 identical jugs and 9 identical cups of water. Since the cups are identical, we can represent the volume of water poured by the cups as 9x, where x is the volume of one cup.
The total volume poured by the jugs and cups is equal to the remaining fraction of the tank: 5/8. This can be represented as:
2 jugs + 9x cups = 5/8
Since the number of cups needed must be an integer, we can assume that x = 1, which means each cup has a volume of 1 unit.
Substituting this value into the equation, we have:
2 jugs + 9 cups = 5/8
To solve for the number of jugs:
2 jugs = 5/8 - 9 = -79/8
Since the number of jugs cannot be negative, it means that there is no valid solution where only cups are used to fill the tank to its brim.
Therefore, there is no solution for the number of identical cups needed to fill the empty tank to its brim using only cups.