PSLEPenelope and Elyse went shopping together with a total amount of $64.80. Penelope spent 2 times as much as Elyse. The amount Elyse had left was $9 more than what she had spent. She had 2 times as much money left as Penelope.
(a) How much money did Elyse spend?
(b) How much money did Penelope have at first?
|
Penelope |
Elyse |
Total |
Before |
2.5 u + 4.5 |
2 u + 9 |
64.80 |
Change |
- 2 u |
- 1 u |
|
After |
0.5 u + 4.5 |
1 u + 9 |
|
(a)
Total amount that Penelope and Elyse had at first
= (2.5 u + 4.5) + (2 u + 9)
= 2.5 u + 2 u + 4.5 + 9
= 4.5 u + 13.5
4.5 u + 13.5 = 64.8
4.5 u = 64.8 - 13.5
4.5 u = 51.3
1 u = 51.3 ÷ 4.5 = 11.4
Amount that Elyse had at first
= 1 u
= $11.40
(b)
Amount that Penelope had at first
= 2.5 u + 4.5
= (2.5 x 11.4) + 4.5
= 28.5 + 4.5
= $33
Answer(s): (a) $11.40; (b) $33