PSLEJane and Emma went shopping together with a total amount of $106.80. Jane spent 2 times as much as Emma. The amount Emma had left was $16 more than what she had spent. She had 2 times as much money left as Jane.
(a) How much money did Emma spend?
(b) How much money did Jane have at first?
|
Jane |
Emma |
Total |
Before |
2.5 u + 8 |
2 u + 16 |
106.80 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 8 |
1 u + 16 |
|
(a)
Total amount that Jane and Emma had at first
= (2.5 u + 8) + (2 u + 16)
= 2.5 u + 2 u + 8 + 16
= 4.5 u + 24
4.5 u + 24 = 106.8
4.5 u = 106.8 - 24
4.5 u = 82.8
1 u = 82.8 ÷ 4.5 = 18.4
Amount that Emma had at first
= 1 u
= $18.40
(b)
Amount that Jane had at first
= 2.5 u + 8
= (2.5 x 18.4) + 8
= 46 + 8
= $54
Answer(s): (a) $18.40; (b) $54