Zara and Erika have some money. If Zara spends $1, she will have
34 as much money as Erika. If Erika spends $4, Zara will have
56 as much money as Erika. How much money does Erika have?
| |
Case 1 |
Case 2 |
| |
Zara |
Erika |
Zara |
Erika |
| Before |
3 u + $1 |
4 u |
5 p |
6 p + $4 |
| Change |
- $1 |
|
|
- $4 |
| After |
3 u |
4 u |
5 p |
6 p |
The amount that Zara has at first in Case 1 and Case 2 is the same.
3 u + 1 = 5 p
3 u = 5 p - 1 --- (1)
The amount that Erika has at first in Case 1 and Case 2 is the same.
4 u = 6 p + 4 --- (2)
Make u the same.
(1)
x 412 u = 20 p - 4 --- (3)
(2)
x 312 u = 18 p + 12 --- (4)
(3) = (4)
20 p - 4 = 18 p + 12
20 p - 18 p = 4 + 12
2 p = 16
1 p = 16 ÷ 2 = 8
Amount that Erika has
= 6 p + 4
= 6 x 8 + 4
= 48 + 4
= $52
Answer(s): $52
