PSLEGwen and Tina went shopping together with a total amount of $90.60. Gwen spent 2 times as much as Tina. The amount Tina had left was $10 more than what she had spent. She had 2 times as much money left as Gwen.
(a) How much money did Tina spend?
(b) How much money did Gwen have at first?
|
Gwen |
Tina |
Total |
Before |
2.5 u + 5 |
2 u + 10 |
90.60 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 5 |
1 u + 10 |
|
(a)
Total amount that Gwen and Tina 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 = 90.6
4.5 u = 90.6 - 15
4.5 u = 75.6
1 u = 75.6 ÷ 4.5 = 16.8
Amount that Tina had at first
= 1 u
= $16.80
(b)
Amount that Gwen had at first
= 2.5 u + 5
= (2.5 x 16.8) + 5
= 42 + 5
= $47
Answer(s): (a) $16.80; (b) $47