Vincent and Kylie has some money each. If Kylie gives Vincent $15, he will have 3 times as much money as her. If Vincent gives Kylie $11, he will have the same amount of money as her. How much money does each person have respectively?
- Vincent?
- Kylie?
| |
Case 1 |
Case 2 |
| |
Vincent |
Kylie |
Vincent |
Kylie |
| Before |
3 u - 15 |
1 u + 15 |
2 u + 11 |
2 u - 11 |
| Change |
+ 15 |
- 15 |
- 11 |
+ 11 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Kylie gives Vincent some money or Vincent gives Kylie some money, the total amount of money remains the same.
Total amount that Vincent and Kylie have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Vincent and Kylie each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Vincent has at first in Case 1 and Case 2 is the same.
3 u - 15 = 2 u + 11
3 u - 2 u = 11 + 15
1 u = 26
Amount that Vincent has
= 2 u + 11
= 2 x 26 + 11
= 52 + 11
= $63
(b)
Amount that Kylie has
= 1 u + 15
= 26 + 15
= $41
Answer(s): (a) $63; (b) $41
