a container has 3/4 gallon of pineapple juice in it. This is 6/7 of the amount originally in the container . How much was originally in the container.
(6/7)x = 3/4
x = (3/4) / (6/7)
x = (3/4) * (7/6)
x = 21/24 = 7/8 gallon
To find out how much juice was originally in the container, we can use a proportion based on the given information.
Let's say the original amount of juice in the container is represented by "x" gallons.
According to the problem, 3/4 gallon is equal to 6/7 of the original amount.
So we can set up the proportion: (3/4) / x = (6/7)
To solve this proportion, we can cross-multiply:
7 * (3/4) = 6 * x
21/4 = 6x
To isolate x, we can multiply both sides by 4/21:
x = (21/4) * (4/21)
x = 1
Therefore, the original amount of juice in the container was 1 gallon.
To find out how much juice was originally in the container, we can set up an equation. Let's represent the original amount of juice in the container as "x".
According to the problem, 3/4 gallon of pineapple juice is equal to 6/7 of the original amount. We can write this as an equation:
3/4 = 6/7 * x
To solve for x, let's isolate it by multiplying both sides of the equation by the reciprocal of 6/7, which is 7/6 (flipping the fraction):
(3/4) * (7/6) = (6/7) * (7/6) * x
(21/24) = (42/42) * x
Simplifying the fraction 21/24 gives us:
7/8 = 1 * x
x = 7/8
Therefore, the original amount of juice in the container was 7/8 gallon.