multiplication and division with fractions

Question

Zoe and Ella had 250 beads altogether.  After Zoe used 18 beads to make a bracelet and Ella gave away 2/5 of her beads, they have the same number of beads left.  How many beads did Zoe have at first?

Answer 1

Z + E = 250

Z-18 = (3/5)E <-- Ella gave away 2/5 of the beads, so she has 3/5 left

Z = (3/5)E + 18

(3/5)E + 18 + E = 250

(3/5)E + 18 + (5/5)E = 250

(8/5)E + 18 = 250

(8/5)E = 232

E = 232*5/8 = 116*5/4 = 58*5/2 = 29*5 = 145

then Z = (3/5)E + 18 = (3/5)(145)+18 = 3*29 +18 = 87+18 = 105

Zoe has 105 and Ella had 145, which is 250 altogether.

Zoe uses 18, so she has 87 left.

Ella gives away (2/5)(145) = 2*29 = 58, so she was 145 - 58 = 87.

So , yes, they both have 87 afterwards.

So the facts check out!

The answers are correct.

Zoe has 105 and Ella had 145