Gwen and Jean have some money. If Gwen spends $14, she will have
25 as much money as Jean. If Jean spends $3, Gwen will have
78 as much money as Jean. How much money does Jean have?
| |
Case 1 |
Case 2 |
| |
Gwen |
Jean |
Gwen |
Jean |
| Before |
2 u + $14 |
5 u |
7 p |
8 p + $3 |
| Change |
- $14 |
|
|
- $3 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Gwen has at first in Case 1 and Case 2 is the same.
2 u + 14 = 7 p
2 u = 7 p - 14 --- (1)
The amount that Jean has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 3 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 70 --- (3)
(2)
x 210 u = 16 p + 6 --- (4)
(3) = (4)
35 p - 70 = 16 p + 6
35 p - 16 p = 70 + 6
19 p = 76
1 p = 76 ÷ 19 = 4
Amount that Jean has
= 8 p + 3
= 8 x 4 + 3
= 32 + 3
= $35
Answer(s): $35
