If Abi gives Tom $16, the amount of money she has will be 30% of his. If Tom gives Abi $110, he will have the same amount of money as her. How much money did each of them have?
(a) Tom
(b) Abi
|
Case 1 |
Case 2 |
|
Tom |
Abi |
Tom |
Abi |
Before |
10 u - 16 |
3 u + 16 |
6.5 u + 110 |
6.5 u - 110 |
Change |
+ 16 |
- 16 |
- 110 |
+ 110 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Abi gives to Tom, there is an internal transfer of money from Abi to Tom. The total amount that both have remains the same.
In Case 2, when Tom gives to Abi, there is an internal transfer of money from Tom to Abi. 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 Abi and Tom have
= 10 u + 3 u
= 13 u
Amount that Abi and Tom each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Tom has at first is the same in Case 1 and Case 2.
10 u - 16 = 6.5 u + 110
10 u - 6.5 u = 110 + 16
3.5 u = 126
1 u = 126 ÷ 3.5 = 36
Amount that Tom has
= 10 u - 16
= 10 x 36 - 16
= 360 - 16
= $344
(b)
Amount that Abi has
= 3 u + 16
= 3 x 36 + 16
= 108 + 16
= $124
Answer(s): (a) $344; (b) $124