Carl and Jen has some money each. If Jen gives Carl $17, he will have 3 times as much money as her. If Carl gives Jen $15, he will have the same amount of money as her. How much money does each person have respectively?
- Carl?
- Jen?
| |
Case 1 |
Case 2 |
| |
Carl |
Jen |
Carl |
Jen |
| Before |
3 u - 17 |
1 u + 17 |
2 u + 15 |
2 u - 15 |
| Change |
+ 17 |
- 17 |
- 15 |
+ 15 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Jen gives Carl some money or Carl gives Jen some money, the total amount of money remains the same.
Total amount that Carl and Jen have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Carl and Jen each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Carl has at first in Case 1 and Case 2 is the same.
3 u - 17 = 2 u + 15
3 u - 2 u = 15 + 17
1 u = 32
Amount that Carl has
= 2 u + 15
= 2 x 32 + 15
= 64 + 15
= $79
(b)
Amount that Jen has
= 1 u + 17
= 32 + 17
= $49
Answer(s): (a) $79; (b) $49
