Jean and Zoe have some money. If Jean spends $4, she will have
35 as much money as Zoe. If Zoe spends $5, Jean will have
56 as much money as Zoe. How much money does Zoe have?
| |
Case 1 |
Case 2 |
| |
Jean |
Zoe |
Jean |
Zoe |
| Before |
3 u + $4 |
5 u |
5 p |
6 p + $5 |
| Change |
- $4 |
|
|
- $5 |
| After |
3 u |
5 u |
5 p |
6 p |
The amount that Jean has at first in Case 1 and Case 2 is the same.
3 u + 4 = 5 p
3 u = 5 p - 4 --- (1)
The amount that Zoe has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 5 --- (2)
Make u the same.
(1)
x 515 u = 25 p - 20 --- (3)
(2)
x 315 u = 18 p + 15 --- (4)
(3) = (4)
25 p - 20 = 18 p + 15
25 p - 18 p = 20 + 15
7 p = 35
1 p = 35 ÷ 7 = 5
Amount that Zoe has
= 6 p + 5
= 6 x 5 + 5
= 30 + 5
= $35
Answer(s): $35
