SOLUTION: Hi Ryan had $120 more than Kaden. Kaden had 1/4 as much as Ryan. Both of them spent a total of $170. As a result Kaden had 2/3 as much as Ryan. A) how much did they have altoget

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Question 1206052: Hi
Ryan had $120 more than Kaden. Kaden had 1/4 as much as Ryan. Both of them spent a total of $170. As a result Kaden had 2/3 as much as Ryan.
A) how much did they have altogether in the end.
B) how much did Kaden have in the end.
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Kaden had 1/4 as mush as Ryan:
let x = amount Kaden had
then 4x = amount Ryan had

Ryan had $120 more than Kaden:
4x = x+120
3x = 120
x = 40

Kaden had x = $40; Ryan had 4x = $160. That's a total of $200.

The two of them spent a total of $170; the amount they had left was $30.

In the end, Kaden had 2/3 as much as Ryan:
let 2x = amount Kaden had at the end
let 3x = amount Ryan had at the end
2x+3x = 30
5x = 30
x = 6

Kaden finished with 2x = $12; Ryan finished with 3x = $18.

ANSWERS:
A) $30
B) $12

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

Hi Ryan had $120 more than Kaden. Kaden had 1/4 as much as Ryan. Both of them spent a total of $170. As a result Kaden had 2/3 as much as Ryan. A) how much did they have altogether in the end. B) how much did Kaden have in the end. Let original amount Kaden had, be K Ryan had $120 more than Kaden. so original amount Ryan had, was K + 120 Also, Kaden had as much as Ryan, so original amount Ryan had, was 4K We now get: K + 120 = 4K 120 = 4K - K 120 = 3K Original amount Kaden had, or Original amount Ryan had: 40 + 120, or 4(40) = $160 Total amount they had, originally: $40 + $160 = $200 Since they spent a total of $170, remainder was $200 - 170 = $30 Let Kaden's remainder be K_r Since in the end, Kaden had as much as Ryan, then Ryan's remainder was of Kaden's, or With total remainder being $30 (see above), we get: ------ Multiplying by LCD, 2 Kaden's remainder, or