If Dana gives Bobby $18, the amount of money she has will be 40% of his. If Bobby gives Dana $12, he will have the same amount of money as her. How much money did each of them have?
(a) Bobby
(b) Dana
|
Case 1 |
Case 2 |
|
Bobby |
Dana |
Bobby |
Dana |
Before |
5 u - 18 |
2 u + 18 |
3.5 u + 12 |
3.5 u - 12 |
Change |
+ 18 |
- 18 |
- 12 |
+ 12 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Dana gives to Bobby, there is an internal transfer of money from Dana to Bobby. The total amount that both have remains the same.
In Case 2, when Bobby gives to Dana, there is an internal transfer of money from Bobby to Dana. 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 Dana and Bobby have
= 5 u + 2 u
= 7 u
Amount that Dana and Bobby each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Bobby has at first is the same in Case 1 and Case 2.
5 u - 18 = 3.5 u + 12
5 u - 3.5 u = 12 + 18
1.5 u = 30
1 u = 30 ÷ 1.5 = 20
Amount that Bobby has
= 5 u - 18
= 5 x 20 - 18
= 100 - 18
= $82
(b)
Amount that Dana has
= 2 u + 18
= 2 x 20 + 18
= 40 + 18
= $58
Answer(s): (a) $82; (b) $58