Xylia and Risa have some money. If Xylia spends $1, she will have
56 as much money as Risa. If Risa spends $2, Xylia will have
78 as much money as Risa. How much money does Risa have?
| |
Case 1 |
Case 2 |
| |
Xylia |
Risa |
Xylia |
Risa |
| Before |
5 u + $1 |
6 u |
7 p |
8 p + $2 |
| Change |
- $1 |
|
|
- $2 |
| After |
5 u |
6 u |
7 p |
8 p |
The amount that Xylia has at first in Case 1 and Case 2 is the same.
5 u + 1 = 7 p
5 u = 7 p - 1 --- (1)
The amount that Risa has at first in Case 1 and Case 2 is the same.
6 u = 8 p + 2 --- (2)
Make u the same.
(1)
x 630 u = 42 p - 6 --- (3)
(2)
x 530 u = 40 p + 10 --- (4)
(3) = (4)
42 p - 6 = 40 p + 10
42 p - 40 p = 6 + 10
2 p = 16
1 p = 16 ÷ 2 = 8
Amount that Risa has
= 8 p + 2
= 8 x 8 + 2
= 64 + 2
= $66
Answer(s): $66
