Erika and Jen have some money. If Erika spends $7, she will have
25 as much money as Jen. If Jen spends $23, Erika will have
58 as much money as Jen. How much money does Jen have?
| |
Case 1 |
Case 2 |
| |
Erika |
Jen |
Erika |
Jen |
| Before |
2 u + $7 |
5 u |
5 p |
8 p + $23 |
| Change |
- $7 |
|
|
- $23 |
| After |
2 u |
5 u |
5 p |
8 p |
The amount that Erika 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 Jen has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 23 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 35 --- (3)
(2)
x 210 u = 16 p + 46 --- (4)
(3) = (4)
25 p - 35 = 16 p + 46
25 p - 16 p = 35 + 46
9 p = 81
1 p = 81 ÷ 9 = 9
Amount that Jen has
= 8 p + 23
= 8 x 9 + 23
= 72 + 23
= $95
Answer(s): $95
