Cole and Rachel has some money each. If Rachel gives Cole $20, he will have 7 times as much money as her. If Cole gives Rachel $12, he will have the same amount of money as her. How much money does each person have respectively?
- Cole?
- Rachel?
|
Case 1 |
Case 2 |
|
Cole |
Rachel |
Cole |
Rachel |
Before |
7 u - 20 |
1 u + 20 |
4 u + 12 |
4 u - 12 |
Change |
+ 20 |
- 20 |
- 12 |
+ 12 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Rachel gives Cole some money or Cole gives Rachel some money, the total amount of money remains the same.
Total amount that Cole and Rachel have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Cole and Rachel 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 - 20 = 4 u + 12
7 u - 4 u = 12 + 20
1 u = 32
Amount that Cole has
= 4 u + 12
= 4 x 32 + 12
= 128 + 12
= $140
(b)
Amount that Rachel has
= 1 u + 20
= 32 + 20
= $52
Answer(s): (a) $140; (b) $52