Joan's Fruit Bowl

Question

Joan's fruit bowl contains only apples and bananas. If Joan randomly selects a piece of fruit from the bowl. The probability it will be a banana is 2/5. However, before she chooses a piece of fruit, Joan throws away 3 bananas. The probability of her choosing a banana is now 1/4. How many apples and bananas were there originally in the bowl?

Answer 1

there are 2 bananas for every 5 apples

2x/5x

throw away 3 bananas

(2x-3)/5x=1x/4x (the new ratio of bananas to apples)

cross multiply

4x(2x-3)=1x(5x)

8x^2-12x=5x^2

8x^2-5x^2-12x=0

3x^2-12x=0

factor

3x(x-4)=0

x-4=0

x=4

4*2=8 bananas originally

4*5=20 apples originally

8/20=2/5

8-3=5

5/20=1/4