PSLEOlivia and Lucy went shopping together with a total amount of $109.80. Olivia spent 2 times as much as Lucy. The amount Lucy had left was $24 more than what she had spent. She had 2 times as much money left as Olivia.
(a) How much money did Lucy spend?
(b) How much money did Olivia have at first?
|
Olivia |
Lucy |
Total |
Before |
2.5 u + 12 |
2 u + 24 |
109.80 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 12 |
1 u + 24 |
|
(a)
Total amount that Olivia and Lucy had at first
= (2.5 u + 12) + (2 u + 24)
= 2.5 u + 2 u + 12 + 24
= 4.5 u + 36
4.5 u + 36 = 109.8
4.5 u = 109.8 - 36
4.5 u = 73.8
1 u = 73.8 ÷ 4.5 = 16.4
Amount that Lucy had at first
= 1 u
= $16.40
(b)
Amount that Olivia had at first
= 2.5 u + 12
= (2.5 x 16.4) + 12
= 41 + 12
= $53
Answer(s): (a) $16.40; (b) $53