PSLETina and Lucy went shopping together with a total amount of $100.80. Tina 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 Tina.
(a) How much money did Lucy spend?
(b) How much money did Tina have at first?
|
Tina |
Lucy |
Total |
Before |
2.5 u + 12 |
2 u + 24 |
100.80 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 12 |
1 u + 24 |
|
(a)
Total amount that Tina 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 = 100.8
4.5 u = 100.8 - 36
4.5 u = 64.8
1 u = 64.8 ÷ 4.5 = 14.4
Amount that Lucy had at first
= 1 u
= $14.40
(b)
Amount that Tina had at first
= 2.5 u + 12
= (2.5 x 14.4) + 12
= 36 + 12
= $48
Answer(s): (a) $14.40; (b) $48