Hazel and Zara have some money. If Hazel spends $4, she will have
35 as much money as Zara. If Zara spends $12, Hazel will have
56 as much money as Zara. How much money does Zara have?
| |
Case 1 |
Case 2 |
| |
Hazel |
Zara |
Hazel |
Zara |
| Before |
3 u + $4 |
5 u |
5 p |
6 p + $12 |
| Change |
- $4 |
|
|
- $12 |
| After |
3 u |
5 u |
5 p |
6 p |
The amount that Hazel 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 Zara has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 12 --- (2)
Make u the same.
(1)
x 515 u = 25 p - 20 --- (3)
(2)
x 315 u = 18 p + 36 --- (4)
(3) = (4)
25 p - 20 = 18 p + 36
25 p - 18 p = 20 + 36
7 p = 56
1 p = 56 ÷ 7 = 8
Amount that Zara has
= 6 p + 12
= 6 x 8 + 12
= 48 + 12
= $60
Answer(s): $60
