Fraction word problem

Question

Sam and Lynn had 96 storybooks altogether. Sam gave 1/4 of his storybooks to Lynn. Lynn then gave 1/3 of the total number of story books she had to Sam. In the end, they had the same number of storybooks. How many storybooks did each of them have at first?

Answer 1

S+L = 96

Sam gave 1/4 of his to Lynn:

(3/4)S + (L + (1/4)S) = 96

Lynn then gave 1/3 of what she has back to Sam, and THOSE two quantities are the same

(3/4)S + (1/3)(L + (1/4)S) = (2/3)(L + (1/4)S)

(3/4)S + (1/3)L + (1/12)S = (2/3)L + (1/6)S

9S + 4L + S = 8L + 2S <--- multiplies by 12

10S + 4L = 8L + 2S

8S - 4L = 0

2S - L = 0

L = 2S

S + L = 96

S + 2S = 96

3S = 96

S = 32

Same had 32 and Lynn had 96-32 = 64

Sam gave 1/4 of his to Lynn....

1/4 of 32 = 8 ---> Sam has 24 and Lynn has 72

Lynn gave 1/3 of hers back to Sam...

1/3 of 72 =24

Sam has 48 and Lynn has 72-24 = 48

So yes it checks

Same had 32 and Lynn had 96-32 = 64