Justin and Gwen has some money each. If Gwen gives Justin $15, he will have 3 times as much money as her. If Justin gives Gwen $18, he will have the same amount of money as her. How much money does each person have respectively?
- Justin?
- Gwen?
|
Case 1 |
Case 2 |
|
Justin |
Gwen |
Justin |
Gwen |
Before |
3 u - 15 |
1 u + 15 |
2 u + 18 |
2 u - 18 |
Change |
+ 15 |
- 15 |
- 18 |
+ 18 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Gwen gives Justin some money or Justin gives Gwen some money, the total amount of money remains the same.
Total amount that Justin and Gwen have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Justin and Gwen each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Justin has at first in Case 1 and Case 2 is the same.
3 u - 15 = 2 u + 18
3 u - 2 u = 18 + 15
1 u = 33
Amount that Justin has
= 2 u + 18
= 2 x 33 + 18
= 66 + 18
= $84
(b)
Amount that Gwen has
= 1 u + 15
= 33 + 15
= $48
Answer(s): (a) $84; (b) $48