Flery has some apples and bananas. The ratio of the apples to the banaas is 2:5. She used 1/4 of the apples to make an apple pie. What is the new ratio of the apples to the bananas?
a/b = 2/5
(3/4 a)/b = (3/4)(a/b) = (3/4)(2/5) = 3/10
To find the new ratio of apples to bananas, we need to determine the number of apples after Flery used 1/4 of them to make an apple pie.
Let's assume that Flery initially had 2x apples and 5x bananas, where x is a common factor.
After using 1/4 of the apples to make the pie, Flery will have 1/4 * 2x = x/2 apples remaining.
Therefore, the new ratio of the apples to the bananas is x/2 : 5x.
However, we want to express this ratio in its simplest form. To do this, we can divide both terms by the greatest common divisor (GCD) of the terms.
In this case, the GCD of x/2 and 5x is x, as x is the only common factor.
Dividing both terms by x, we get:
(x/2) ÷ x = 1/2
(5x) ÷ x = 5
Therefore, the new ratio of the apples to the bananas is 1/2 : 5, or simply 1 : 10.