PSLEXuan and Sarah went shopping together with a total amount of $97.80. Xuan spent 2 times as much as Sarah. The amount Sarah had left was $25 more than what she had spent. She had 2 times as much money left as Xuan.
(a) How much money did Sarah spend?
(b) How much money did Xuan have at first?
|
Xuan |
Sarah |
Total |
Before |
2.5 u + 12.5 |
2 u + 25 |
97.80 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 12.5 |
1 u + 25 |
|
(a)
Total amount that Xuan and Sarah had at first
= (2.5 u + 12.5) + (2 u + 25)
= 2.5 u + 2 u + 12.5 + 25
= 4.5 u + 37.5
4.5 u + 37.5 = 97.8
4.5 u = 97.8 - 37.5
4.5 u = 60.3
1 u = 60.3 ÷ 4.5 = 13.4
Amount that Sarah had at first
= 1 u
= $13.40
(b)
Amount that Xuan had at first
= 2.5 u + 12.5
= (2.5 x 13.4) + 12.5
= 33.5 + 12.5
= $46
Answer(s): (a) $13.40; (b) $46