Shiyun and Opal have some money. If Shiyun spends $16, she will have
25 as much money as Opal. If Opal spends $12, Shiyun will have
56 as much money as Opal. How much money does Opal have?
| |
Case 1 |
Case 2 |
| |
Shiyun |
Opal |
Shiyun |
Opal |
| Before |
2 u + $16 |
5 u |
5 p |
6 p + $12 |
| Change |
- $16 |
|
|
- $12 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Shiyun has at first in Case 1 and Case 2 is the same.
2 u + 16 = 5 p
2 u = 5 p - 16 --- (1)
The amount that Opal has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 12 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 80 --- (3)
(2)
x 210 u = 12 p + 24 --- (4)
(3) = (4)
25 p - 80 = 12 p + 24
25 p - 12 p = 80 + 24
13 p = 104
1 p = 104 ÷ 13 = 8
Amount that Opal has
= 6 p + 12
= 6 x 8 + 12
= 48 + 12
= $60
Answer(s): $60
