Xandra and Jen have some money. If Xandra spends $8, she will have
25 as much money as Jen. If Jen spends $12, Xandra will have
67 as much money as Jen. How much money does Jen have?
| |
Case 1 |
Case 2 |
| |
Xandra |
Jen |
Xandra |
Jen |
| Before |
2 u + $8 |
5 u |
6 p |
7 p + $12 |
| Change |
- $8 |
|
|
- $12 |
| After |
2 u |
5 u |
6 p |
7 p |
The amount that Xandra has at first in Case 1 and Case 2 is the same.
2 u + 8 = 6 p
2 u = 6 p - 8 --- (1)
The amount that Jen has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 12 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 40 --- (3)
(2)
x 210 u = 14 p + 24 --- (4)
(3) = (4)
30 p - 40 = 14 p + 24
30 p - 14 p = 40 + 24
16 p = 64
1 p = 64 ÷ 16 = 4
Amount that Jen has
= 7 p + 12
= 7 x 4 + 12
= 28 + 12
= $40
Answer(s): $40
