PSLERisa and Raeann went shopping together with a total amount of $79.80. Risa spent 2 times as much as Raeann. The amount Raeann had left was $10 more than what she had spent. She had 2 times as much money left as Risa.
(a) How much money did Raeann spend?
(b) How much money did Risa have at first?
|
Risa |
Raeann |
Total |
Before |
2.5 u + 5 |
2 u + 10 |
79.80 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 5 |
1 u + 10 |
|
(a)
Total amount that Risa and Raeann 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 = 79.8
4.5 u = 79.8 - 15
4.5 u = 64.8
1 u = 64.8 ÷ 4.5 = 14.4
Amount that Raeann had at first
= 1 u
= $14.40
(b)
Amount that Risa had at first
= 2.5 u + 5
= (2.5 x 14.4) + 5
= 36 + 5
= $41
Answer(s): (a) $14.40; (b) $41