If Betty gives Tim $27, the amount of money she has will be 10% of his. If Tim gives Betty $189, he will have the same amount of money as her. How much money did each of them have?
(a) Tim
(b) Betty
|
Case 1 |
Case 2 |
|
Tim |
Betty |
Tim |
Betty |
Before |
10 u - 27 |
1 u + 27 |
5.5 u + 189 |
5.5 u - 189 |
Change |
+ 27 |
- 27 |
- 189 |
+ 189 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Betty gives to Tim, there is an internal transfer of money from Betty to Tim. The total amount that both have remains the same.
In Case 2, when Tim gives to Betty, there is an internal transfer of money from Tim to Betty. 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 Betty and Tim have
= 10 u + 1 u
= 11 u
Amount that Betty and Tim each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Tim has at first is the same in Case 1 and Case 2.
10 u - 27 = 5.5 u + 189
10 u - 5.5 u = 189 + 27
4.5 u = 216
1 u = 216 ÷ 4.5 = 48
Amount that Tim has
= 10 u - 27
= 10 x 48 - 27
= 480 - 27
= $453
(b)
Amount that Betty has
= 1 u + 27
= 1 x 48 + 27
= 48 + 27
= $75
Answer(s): (a) $453; (b) $75