PSLELynn and Zoe went shopping together with a total amount of $115.80. Lynn spent 2 times as much as Zoe. The amount Zoe had left was $31 more than what she had spent. She had 2 times as much money left as Lynn.
(a) How much money did Zoe spend?
(b) How much money did Lynn have at first?
|
Lynn |
Zoe |
Total |
Before |
2.5 u + 15.5 |
2 u + 31 |
115.80 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 15.5 |
1 u + 31 |
|
(a)
Total amount that Lynn and Zoe had at first
= (2.5 u + 15.5) + (2 u + 31)
= 2.5 u + 2 u + 15.5 + 31
= 4.5 u + 46.5
4.5 u + 46.5 = 115.8
4.5 u = 115.8 - 46.5
4.5 u = 69.3
1 u = 69.3 ÷ 4.5 = 15.4
Amount that Zoe had at first
= 1 u
= $15.40
(b)
Amount that Lynn had at first
= 2.5 u + 15.5
= (2.5 x 15.4) + 15.5
= 38.5 + 15.5
= $54
Answer(s): (a) $15.40; (b) $54