Zoe and Opal have some money. If Zoe spends $13, she will have
25 as much money as Opal. If Opal spends $34, Zoe will have
78 as much money as Opal. How much money does Zoe have?
| |
Case 1 |
Case 2 |
| |
Zoe |
Opal |
Zoe |
Opal |
| Before |
2 u + $13 |
5 u |
7 p |
8 p + $34 |
| Change |
- $13 |
|
|
- $34 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Zoe has at first in Case 1 and Case 2 is the same.
2 u + 13 = 7 p
2 u = 7 p - 13 --- (1)
The amount that Opal has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 34 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 65 --- (3)
(2)
x 210 u = 16 p + 68 --- (4)
(3) = (4)
35 p - 65 = 16 p + 68
35 p - 16 p = 65 + 68
19 p = 133
1 p = 133 ÷ 19 = 7
Amount that Zoe has
= 7 p
= 7 x 7
= $49
Answer(s): $49
