PSLERachel and Gem went shopping together with a total amount of $88.80. Rachel spent 2 times as much as Gem. The amount Gem had left was $16 more than what she had spent. She had 2 times as much money left as Rachel.
(a) How much money did Gem spend?
(b) How much money did Rachel have at first?
|
Rachel |
Gem |
Total |
Before |
2.5 u + 8 |
2 u + 16 |
88.80 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 8 |
1 u + 16 |
|
(a)
Total amount that Rachel and Gem had at first
= (2.5 u + 8) + (2 u + 16)
= 2.5 u + 2 u + 8 + 16
= 4.5 u + 24
4.5 u + 24 = 88.8
4.5 u = 88.8 - 24
4.5 u = 64.8
1 u = 64.8 ÷ 4.5 = 14.4
Amount that Gem had at first
= 1 u
= $14.40
(b)
Amount that Rachel had at first
= 2.5 u + 8
= (2.5 x 14.4) + 8
= 36 + 8
= $44
Answer(s): (a) $14.40; (b) $44