Cole and Raeann has some money each. If Raeann gives Cole $12, he will have 7 times as much money as her. If Cole gives Raeann $16, he will have the same amount of money as her. How much money does each person have respectively?
- Cole?
- Raeann?
| |
Case 1 |
Case 2 |
| |
Cole |
Raeann |
Cole |
Raeann |
| Before |
7 u - 12 |
1 u + 12 |
4 u + 16 |
4 u - 16 |
| Change |
+ 12 |
- 12 |
- 16 |
+ 16 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Raeann gives Cole some money or Cole gives Raeann some money, the total amount of money remains the same.
Total amount that Cole and Raeann have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Cole and Raeann each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Cole has at first in Case 1 and Case 2 is the same.
7 u - 12 = 4 u + 16
7 u - 4 u = 16 + 12
1 u = 28
Amount that Cole has
= 4 u + 16
= 4 x 28 + 16
= 112 + 16
= $128
(b)
Amount that Raeann has
= 1 u + 12
= 28 + 12
= $40
Answer(s): (a) $128; (b) $40
