Gwen and Irene have some money. If Gwen spends $19, she will have
25 as much money as Irene. If Irene spends $2, Gwen will have
57 as much money as Irene. How much money does Irene have?
| |
Case 1 |
Case 2 |
| |
Gwen |
Irene |
Gwen |
Irene |
| Before |
2 u + $19 |
5 u |
5 p |
7 p + $2 |
| Change |
- $19 |
|
|
- $2 |
| After |
2 u |
5 u |
5 p |
7 p |
The amount that Gwen has at first in Case 1 and Case 2 is the same.
2 u + 19 = 5 p
2 u = 5 p - 19 --- (1)
The amount that Irene has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 2 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 95 --- (3)
(2)
x 210 u = 14 p + 4 --- (4)
(3) = (4)
25 p - 95 = 14 p + 4
25 p - 14 p = 95 + 4
11 p = 99
1 p = 99 ÷ 11 = 9
Amount that Irene has
= 7 p + 2
= 7 x 9 + 2
= 63 + 2
= $65
Answer(s): $65
