Before and After - Change Unknown

Question

Ryan had $120 more than Kaden. Kaden had 1/4 as much money as Ryan. Both of them spent a total of $170 on some gifts for their friends. As a result, Kaden had 2/3 as much as Ryan.

(a) How much do they have altogether in the end?

(b) How much did Kaden have in the end?

Answer 1

The $120 in excess that Ryan has is 3 times what Kaden has.

Kaden has $40 to start. Ryan has $160.

What they spent

K + R = 170

R = 170 - K

(40 - K) / (160 - (170 - K)) = 2 / 3

(40 - K) / (-10 + K) = 2 / 3

3(40 - K) = 2(-10 + K)

120 - 3K = -20 + 2K

140 = 5K

28 = K

Kaden now has $40 - $28

Ryan now has $160 - ($170 - $28)