Cole and Olivia has some money each. If Olivia gives Cole $17, he will have 3 times as much money as her. If Cole gives Olivia $19, he will have the same amount of money as her. How much money does each person have respectively?
- Cole?
- Olivia?
|
Case 1 |
Case 2 |
|
Cole |
Olivia |
Cole |
Olivia |
Before |
3 u - 17 |
1 u + 17 |
2 u + 19 |
2 u - 19 |
Change |
+ 17 |
- 17 |
- 19 |
+ 19 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Olivia gives Cole some money or Cole gives Olivia some money, the total amount of money remains the same.
Total amount that Cole and Olivia have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Cole and Olivia each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Cole has at first in Case 1 and Case 2 is the same.
3 u - 17 = 2 u + 19
3 u - 2 u = 19 + 17
1 u = 36
Amount that Cole has
= 2 u + 19
= 2 x 36 + 19
= 72 + 19
= $91
(b)
Amount that Olivia has
= 1 u + 17
= 36 + 17
= $53
Answer(s): (a) $91; (b) $53