If Vanessa gives George $14, the amount of money she has will be 10% of his. If George gives Vanessa $121, he will have the same amount of money as her. How much money did each of them have?
(a) George
(b) Vanessa
|
Case 1 |
Case 2 |
|
George |
Vanessa |
George |
Vanessa |
Before |
10 u - 14 |
1 u + 14 |
5.5 u + 121 |
5.5 u - 121 |
Change |
+ 14 |
- 14 |
- 121 |
+ 121 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Vanessa gives to George, there is an internal transfer of money from Vanessa to George. The total amount that both have remains the same.
In Case 2, when George gives to Vanessa, there is an internal transfer of money from George to Vanessa. The total amount that both have remains the same.
The total amount that both have in Case 1 and Case 2 are the same.
Total amount that Vanessa and George have
= 10 u + 1 u
= 11 u
Amount that Vanessa and George each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that George has at first is the same in Case 1 and Case 2.
10 u - 14 = 5.5 u + 121
10 u - 5.5 u = 121 + 14
4.5 u = 135
1 u = 135 ÷ 4.5 = 30
Amount that George has
= 10 u - 14
= 10 x 30 - 14
= 300 - 14
= $286
(b)
Amount that Vanessa has
= 1 u + 14
= 1 x 30 + 14
= 30 + 14
= $44
Answer(s): (a) $286; (b) $44