PSLEOlivia and Anna went shopping together with a total amount of $106.20. Olivia spent 2 times as much as Anna. The amount Anna had left was $30 more than what she had spent. She had 2 times as much money left as Olivia.
(a) How much money did Anna spend?
(b) How much money did Olivia have at first?
|
Olivia |
Anna |
Total |
Before |
2.5 u + 15 |
2 u + 30 |
106.20 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 15 |
1 u + 30 |
|
(a)
Total amount that Olivia and Anna had at first
= (2.5 u + 15) + (2 u + 30)
= 2.5 u + 2 u + 15 + 30
= 4.5 u + 45
4.5 u + 45 = 106.2
4.5 u = 106.2 - 45
4.5 u = 61.2
1 u = 61.2 ÷ 4.5 = 13.6
Amount that Anna had at first
= 1 u
= $13.60
(b)
Amount that Olivia had at first
= 2.5 u + 15
= (2.5 x 13.6) + 15
= 34 + 15
= $49
Answer(s): (a) $13.60; (b) $49