Flery has some apples and bananas. The ratio of the apples to the bananas is 2:5. She used 1/4 of the apples to make an apple pie. What is the ratio of the apples to the bananas?
To find the new ratio of apples to bananas after using 1/4 of the apples to make an apple pie, we'll first need to determine the quantities of apples and bananas we're working with.
Let's say Flery initially has 2x apples and 5x bananas. Since the ratio of apples to bananas is 2:5, we can represent this as 2x:5x.
We're told that Flery used 1/4 of the apples to make an apple pie. This means she used 1/4 * 2x = 1/2x apples for the pie.
Now let's calculate the remaining quantity of apples. Initially, she had 2x apples, and she used 1/2x for the pie. So she has 2x - 1/2x = 3/2x apples left.
Therefore, the new ratio of apples to bananas is 3/2x:5x.
To simplify the ratio, we can divide both the numerator and denominator by the greatest common divisor (GCD) of 3/2x and 5x. In this case, the GCD is x.
Dividing both terms of the ratio by x, we get:
(3/2x)/(x) : (5x)/(x)
= 3/2 : 5
So, the simplified ratio of the remaining apples to bananas is 3:5.
To calculate the new ratio of apples to bananas after Flery used 1/4 of the apples to make an apple pie, we need to subtract the number of apples used for the pie from the total number of apples.
Let's assume Flery initially had 2x apples and 5x bananas.
She used 1/4 of the apples for the pie, which is (1/4) * 2x = 1/2 * x apple.
So, she has 2x - (1/2 * x) apples remaining.
The new ratio of apples to bananas is (2x - (1/2 * x)) : 5x.
To simplify the ratio, we can find a common denominator:
(2x - (1/2 * x)) : 5x
= (4x/2 - (1/2 * x)) : 5x
= ((4x - x/2)) : 5x
= (8x/2 - x/2) : 5x
= (7x/2) : 5x
= 7 : 10 or 7/10
Therefore, the new ratio of apples to bananas after Flery used 1/4 of the apples to make an apple pie is 7:10 or 7/10.