PSLEUsha and Xandra went shopping together with a total amount of $99.60. Usha spent 2 times as much as Xandra. The amount Xandra had left was $10 more than what she had spent. She had 2 times as much money left as Usha.
(a) How much money did Xandra spend?
(b) How much money did Usha have at first?
|
Usha |
Xandra |
Total |
Before |
2.5 u + 5 |
2 u + 10 |
99.60 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 5 |
1 u + 10 |
|
(a)
Total amount that Usha and Xandra had at first
= (2.5 u + 5) + (2 u + 10)
= 2.5 u + 2 u + 5 + 10
= 4.5 u + 15
4.5 u + 15 = 99.6
4.5 u = 99.6 - 15
4.5 u = 84.6
1 u = 84.6 ÷ 4.5 = 18.8
Amount that Xandra had at first
= 1 u
= $18.80
(b)
Amount that Usha had at first
= 2.5 u + 5
= (2.5 x 18.8) + 5
= 47 + 5
= $52
Answer(s): (a) $18.80; (b) $52