Riordan and Risa has some money each. If Risa gives Riordan $18, he will have 7 times as much money as her. If Riordan gives Risa $13, he will have the same amount of money as her. How much money does each person have respectively?
- Riordan?
- Risa?
| |
Case 1 |
Case 2 |
| |
Riordan |
Risa |
Riordan |
Risa |
| Before |
7 u - 18 |
1 u + 18 |
4 u + 13 |
4 u - 13 |
| Change |
+ 18 |
- 18 |
- 13 |
+ 13 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Risa gives Riordan some money or Riordan gives Risa some money, the total amount of money remains the same.
Total amount that Riordan and Risa have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Riordan and Risa each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Riordan has at first in Case 1 and Case 2 is the same.
7 u - 18 = 4 u + 13
7 u - 4 u = 13 + 18
1 u = 31
Amount that Riordan has
= 4 u + 13
= 4 x 31 + 13
= 124 + 13
= $137
(b)
Amount that Risa has
= 1 u + 18
= 31 + 18
= $49
Answer(s): (a) $137; (b) $49
