PSLENicole and Gem went shopping together with a total amount of $81.60. Nicole 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 Nicole.
(a) How much money did Gem spend?
(b) How much money did Nicole have at first?
|
Nicole |
Gem |
Total |
Before |
2.5 u + 8 |
2 u + 16 |
81.60 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 8 |
1 u + 16 |
|
(a)
Total amount that Nicole 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 = 81.6
4.5 u = 81.6 - 24
4.5 u = 57.6
1 u = 57.6 ÷ 4.5 = 12.8
Amount that Gem had at first
= 1 u
= $12.80
(b)
Amount that Nicole had at first
= 2.5 u + 8
= (2.5 x 12.8) + 8
= 32 + 8
= $40
Answer(s): (a) $12.80; (b) $40