Opal and Xandra have some money. If Opal spends $3, she will have
35 as much money as Xandra. If Xandra spends $16, Opal will have
67 as much money as Xandra. How much money does Opal have?
| |
Case 1 |
Case 2 |
| |
Opal |
Xandra |
Opal |
Xandra |
| Before |
3 u + $3 |
5 u |
6 p |
7 p + $16 |
| Change |
- $3 |
|
|
- $16 |
| After |
3 u |
5 u |
6 p |
7 p |
The amount that Opal has at first in Case 1 and Case 2 is the same.
3 u + 3 = 6 p
3 u = 6 p - 3 --- (1)
The amount that Xandra has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 16 --- (2)
Make u the same.
(1)
x 515 u = 30 p - 15 --- (3)
(2)
x 315 u = 21 p + 48 --- (4)
(3) = (4)
30 p - 15 = 21 p + 48
30 p - 21 p = 15 + 48
9 p = 63
1 p = 63 ÷ 9 = 7
Amount that Opal has
= 6 p
= 6 x 7
= $42
Answer(s): $42
