A farm stand sells cider from two bar ells.The smaller barrel holds 336 L, but it is now 5/6 full. The farmer empties this cider into the other barrel and finds that the cider fills only 4/9 of it. How much cider would the larger barrel hold when full?
My guess 404
The smaller barrel holds 336 L, but it is only 5/6 full.
1/6 of 336 is 336/6 = 56 L
So 5/6 of 336 is 5 times this amount:
5 x 56 = 280 L of apple cider in the smaller barrel.
The 280 L is now poured into the larger barrel.
This 280 L fills 4/9 of the barrel.
Find how much fills 1/9 of the barrel:
280/4 = 70 L
If 70 L fills 1/9 of the barrel, then 70 x 9 = 630 L fills 9/9 of the barrel (i.e. fills the whole barrel).
Let's break down the problem step by step.
Step 1: Calculate the amount of cider in the smaller barrel.
The smaller barrel is 5/6 full, which means there is (1 - 5/6) = 1/6 of the barrel empty.
Since the smaller barrel can hold 336 liters, the amount of cider in it is 336 * (5/6) = 280 liters.
Step 2: Calculate the volume of the larger barrel.
When the cider from the smaller barrel is transferred into the larger barrel, it fills only 4/9 of the larger barrel.
Let's assume the volume of the larger barrel is x liters.
So, 4/9 of the larger barrel is (4/9) * x liters.
Step 3: Set up an equation and solve for x.
According to the problem, the amount of cider in the smaller barrel (280 liters) equals 4/9 of the larger barrel.
280 = (4/9) * x
To solve for x, we can multiply both sides of the equation by 9/4 to get rid of the fraction:
x = (280 * 9/4) = 630
Therefore, the larger barrel can hold 630 liters of cider when full.
So, your guess of 404 liters is not correct. The correct answer is 630 liters.
To determine the capacity of the larger barrel, we first need to find out the remaining capacity of the smaller barrel.
We know that the smaller barrel is currently 5/6 full and has a capacity of 336 liters. So, the amount of cider currently in the smaller barrel is:
5/6 * 336 = 280 liters
Since the remaining cider is transferred to the larger barrel, it fills only 4/9 of it. Let's assume the capacity of the larger barrel is x liters. Therefore, the amount of cider in the larger barrel is:
4/9 * x = 280
To find x, we can multiply both sides of the equation by 9/4:
(4/9) * (9/4) * x = (280) * (9/4)
x = (280) * (9/4) * (9/4)
x = 630
Therefore, the larger barrel can hold 630 liters when full, not 404 liters as you guessed.