If Penelope gives Warren $19, the amount of money she has will be 80% of his. If Warren gives Penelope $3, he will have the same amount of money as her. How much money did each of them have?
(a) Warren
(b) Penelope
|
Case 1 |
Case 2 |
|
Warren |
Penelope |
Warren |
Penelope |
Before |
5 u - 19 |
4 u + 19 |
4.5 u + 3 |
4.5 u - 3 |
Change |
+ 19 |
- 19 |
- 3 |
+ 3 |
After |
5 u |
4 u |
4.5 u |
4.5 u |
(a)
80% =
80100 =
45 In Case 1, when Penelope gives to Warren, there is an internal transfer of money from Penelope to Warren. The total amount that both have remains the same.
In Case 2, when Warren gives to Penelope, there is an internal transfer of money from Warren to Penelope. 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 Penelope and Warren have
= 5 u + 4 u
= 9 u
Amount that Penelope and Warren each has in the end for Case 2
= 9 u ÷ 2
= 4.5 u
Amount that Warren has at first is the same in Case 1 and Case 2.
5 u - 19 = 4.5 u + 3
5 u - 4.5 u = 3 + 19
0.5 u = 22
1 u = 22 ÷ 0.5 = 44
Amount that Warren has
= 5 u - 19
= 5 x 44 - 19
= 220 - 19
= $201
(b)
Amount that Penelope has
= 4 u + 19
= 4 x 44 + 19
= 176 + 19
= $195
Answer(s): (a) $201; (b) $195