Cole and Yen has some money each. If Yen gives Cole $18, he will have 3 times as much money as her. If Cole gives Yen $17, he will have the same amount of money as her. How much money does each person have respectively?
- Cole?
- Yen?
| |
Case 1 |
Case 2 |
| |
Cole |
Yen |
Cole |
Yen |
| Before |
3 u - 18 |
1 u + 18 |
2 u + 17 |
2 u - 17 |
| Change |
+ 18 |
- 18 |
- 17 |
+ 17 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Yen gives Cole some money or Cole gives Yen some money, the total amount of money remains the same.
Total amount that Cole and Yen have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Cole and Yen 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 - 18 = 2 u + 17
3 u - 2 u = 17 + 18
1 u = 35
Amount that Cole has
= 2 u + 17
= 2 x 35 + 17
= 70 + 17
= $87
(b)
Amount that Yen has
= 1 u + 18
= 35 + 18
= $53
Answer(s): (a) $87; (b) $53
