Cole and Victoria has some money each. If Victoria gives Cole $19, he will have 5 times as much money as her. If Cole gives Victoria $12, he will have the same amount of money as her. How much money does each person have respectively?
- Cole?
- Victoria?
| |
Case 1 |
Case 2 |
| |
Cole |
Victoria |
Cole |
Victoria |
| Before |
5 u - 19 |
1 u + 19 |
3 u + 12 |
3 u - 12 |
| Change |
+ 19 |
- 19 |
- 12 |
+ 12 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Victoria gives Cole some money or Cole gives Victoria some money, the total amount of money remains the same.
Total amount that Cole and Victoria have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Cole and Victoria each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Cole has at first in Case 1 and Case 2 is the same.
5 u - 19 = 3 u + 12
5 u - 3 u = 12 + 19
1 u = 31
Amount that Cole has
= 3 u + 12
= 3 x 31 + 12
= 93 + 12
= $105
(b)
Amount that Victoria has
= 1 u + 19
= 31 + 19
= $50
Answer(s): (a) $105; (b) $50
