There were 90 cookies in a box. The number of raisin cookies was 2/3 the number of plain cookies. Chantalle ate an equal number of raisin and plain cookies. As a result, the ratio of the number of raisin cookies to the total number of cookies left was 1 : 5. How many cookies did Chantalle eat?

Answer 1

Original:
plain + 2/3 plain = 90
5/3 plain = 90
plain = 54
raisin = 90 - 54 = 36
=====================
final
hc = half the number he ate
54 - hc = plain left
36 - hc = raisin left
------------------------- add
90 - 2 hc = total left
================
so
(36 - hc) / (90-2 hc) = 1/5
(36 - hc) 5 = 90 - 2 hc
90 = 3 hc
hc = 30
so he ate 2 * 30 = 60