Rachel and Jean have some money. If Rachel spends $19, she will have
25 as much money as Jean. If Jean spends $2, Rachel will have
58 as much money as Jean. How much money does Rachel have?
| |
Case 1 |
Case 2 |
| |
Rachel |
Jean |
Rachel |
Jean |
| Before |
2 u + $19 |
5 u |
5 p |
8 p + $2 |
| Change |
- $19 |
|
|
- $2 |
| After |
2 u |
5 u |
5 p |
8 p |
The amount that Rachel 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 Jean has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 2 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 95 --- (3)
(2)
x 210 u = 16 p + 4 --- (4)
(3) = (4)
25 p - 95 = 16 p + 4
25 p - 16 p = 95 + 4
9 p = 99
1 p = 99 ÷ 9 = 11
Amount that Rachel has
= 5 p
= 5 x 11
= $55
Answer(s): $55
