Jean and Rachel have some money. If Jean spends $7, she will have
25 as much money as Rachel. If Rachel spends $15, Jean will have
56 as much money as Rachel. How much money does Jean have?
| |
Case 1 |
Case 2 |
| |
Jean |
Rachel |
Jean |
Rachel |
| Before |
2 u + $7 |
5 u |
5 p |
6 p + $15 |
| Change |
- $7 |
|
|
- $15 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Jean has at first in Case 1 and Case 2 is the same.
2 u + 7 = 5 p
2 u = 5 p - 7 --- (1)
The amount that Rachel has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 15 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 35 --- (3)
(2)
x 210 u = 12 p + 30 --- (4)
(3) = (4)
25 p - 35 = 12 p + 30
25 p - 12 p = 35 + 30
13 p = 65
1 p = 65 ÷ 13 = 5
Amount that Jean has
= 5 p
= 5 x 5
= $25
Answer(s): $25
