PSLENicole and Xandra went shopping together with a total amount of $109.20. Nicole spent 2 times as much as Xandra. The amount Xandra had left was $23 more than what she had spent. She had 2 times as much money left as Nicole.
(a) How much money did Xandra spend?
(b) How much money did Nicole have at first?
|
Nicole |
Xandra |
Total |
Before |
2.5 u + 11.5 |
2 u + 23 |
109.20 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 11.5 |
1 u + 23 |
|
(a)
Total amount that Nicole and Xandra had at first
= (2.5 u + 11.5) + (2 u + 23)
= 2.5 u + 2 u + 11.5 + 23
= 4.5 u + 34.5
4.5 u + 34.5 = 109.2
4.5 u = 109.2 - 34.5
4.5 u = 74.7
1 u = 74.7 ÷ 4.5 = 16.6
Amount that Xandra had at first
= 1 u
= $16.60
(b)
Amount that Nicole had at first
= 2.5 u + 11.5
= (2.5 x 16.6) + 11.5
= 41.5 + 11.5
= $53
Answer(s): (a) $16.60; (b) $53