Ryan and Shiyun has some money each. If Shiyun gives Ryan $17, he will have 3 times as much money as her. If Ryan gives Shiyun $10, he will have the same amount of money as her. How much money does each person have respectively?
- Ryan?
- Shiyun?
|
Case 1 |
Case 2 |
|
Ryan |
Shiyun |
Ryan |
Shiyun |
Before |
3 u - 17 |
1 u + 17 |
2 u + 10 |
2 u - 10 |
Change |
+ 17 |
- 17 |
- 10 |
+ 10 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Shiyun gives Ryan some money or Ryan gives Shiyun some money, the total amount of money remains the same.
Total amount that Ryan and Shiyun have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Ryan and Shiyun each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Ryan has at first in Case 1 and Case 2 is the same.
3 u - 17 = 2 u + 10
3 u - 2 u = 10 + 17
1 u = 27
Amount that Ryan has
= 2 u + 10
= 2 x 27 + 10
= 54 + 10
= $64
(b)
Amount that Shiyun has
= 1 u + 17
= 27 + 17
= $44
Answer(s): (a) $64; (b) $44