Rael and Kimberly has some money each. If Kimberly gives Rael $17, he will have 5 times as much money as her. If Rael gives Kimberly $10, he will have the same amount of money as her. How much money does each person have respectively?
- Rael?
- Kimberly?
| |
Case 1 |
Case 2 |
| |
Rael |
Kimberly |
Rael |
Kimberly |
| Before |
5 u - 17 |
1 u + 17 |
3 u + 10 |
3 u - 10 |
| Change |
+ 17 |
- 17 |
- 10 |
+ 10 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Kimberly gives Rael some money or Rael gives Kimberly some money, the total amount of money remains the same.
Total amount that Rael and Kimberly have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Rael and Kimberly each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Rael has at first in Case 1 and Case 2 is the same.
5 u - 17 = 3 u + 10
5 u - 3 u = 10 + 17
1 u = 27
Amount that Rael has
= 3 u + 10
= 3 x 27 + 10
= 81 + 10
= $91
(b)
Amount that Kimberly has
= 1 u + 17
= 27 + 17
= $44
Answer(s): (a) $91; (b) $44
