Jane and David shared some pencils in the ratio 5:7. David gave 3/7 of his pencils to Jane. What is the new ratio of Jane's and David's pencils? Give your answer in the simplest form.

Answer 1

J/D =5/7 so D = 7 J / 5
Dnew = (4/7) D = 4 J/5
Jnew = J + (3/7) D = J + (3/7)(7/5) J = J +(3/5)J = (8/5)J
Jnew / Dnew = (8/5) J / (4/5)J = 2

Answer 2

pencils owed by
Jane --- 5x
David --- 7x

after the gifting:
David --- (4/7)(7x) = 4x
Jane ---- 5x + (3/7)(7x) = 8x

new ratio:
Jane : David = 8x : 4x = 2 : 1