PSLEGem and Rachel went shopping together with a total amount of $117.60. Gem spent 2 times as much as Rachel. The amount Rachel had left was $37 more than what she had spent. She had 2 times as much money left as Gem.
(a) How much money did Rachel spend?
(b) How much money did Gem have at first?
|
Gem |
Rachel |
Total |
Before |
2.5 u + 18.5 |
2 u + 37 |
117.60 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 18.5 |
1 u + 37 |
|
(a)
Total amount that Gem and Rachel had at first
= (2.5 u + 18.5) + (2 u + 37)
= 2.5 u + 2 u + 18.5 + 37
= 4.5 u + 55.5
4.5 u + 55.5 = 117.6
4.5 u = 117.6 - 55.5
4.5 u = 62.1
1 u = 62.1 ÷ 4.5 = 13.8
Amount that Rachel had at first
= 1 u
= $13.80
(b)
Amount that Gem had at first
= 2.5 u + 18.5
= (2.5 x 13.8) + 18.5
= 34.5 + 18.5
= $53
Answer(s): (a) $13.80; (b) $53