Elijah and Winnie has some money each. If Winnie gives Elijah $20, he will have 3 times as much money as her. If Elijah gives Winnie $18, he will have the same amount of money as her. How much money does each person have respectively?
- Elijah?
- Winnie?
|
Case 1 |
Case 2 |
|
Elijah |
Winnie |
Elijah |
Winnie |
Before |
3 u - 20 |
1 u + 20 |
2 u + 18 |
2 u - 18 |
Change |
+ 20 |
- 20 |
- 18 |
+ 18 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Winnie gives Elijah some money or Elijah gives Winnie some money, the total amount of money remains the same.
Total amount that Elijah and Winnie have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Elijah and Winnie each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Elijah has at first in Case 1 and Case 2 is the same.
3 u - 20 = 2 u + 18
3 u - 2 u = 18 + 20
1 u = 38
Amount that Elijah has
= 2 u + 18
= 2 x 38 + 18
= 76 + 18
= $94
(b)
Amount that Winnie has
= 1 u + 20
= 38 + 20
= $58
Answer(s): (a) $94; (b) $58