Vincent and Hilda has some money each. If Hilda gives Vincent $20, he will have 3 times as much money as her. If Vincent gives Hilda $13, he will have the same amount of money as her. How much money does each person have respectively?
- Vincent?
- Hilda?
| |
Case 1 |
Case 2 |
| |
Vincent |
Hilda |
Vincent |
Hilda |
| Before |
3 u - 20 |
1 u + 20 |
2 u + 13 |
2 u - 13 |
| Change |
+ 20 |
- 20 |
- 13 |
+ 13 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Hilda gives Vincent some money or Vincent gives Hilda some money, the total amount of money remains the same.
Total amount that Vincent and Hilda have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Vincent and Hilda 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 - 20 = 2 u + 13
3 u - 2 u = 13 + 20
1 u = 33
Amount that Vincent has
= 2 u + 13
= 2 x 33 + 13
= 66 + 13
= $79
(b)
Amount that Hilda has
= 1 u + 20
= 33 + 20
= $53
Answer(s): (a) $79; (b) $53
