Japheth and Jaslyn has some money each. If Jaslyn gives Japheth $10, he will have 7 times as much money as her. If Japheth gives Jaslyn $12, he will have the same amount of money as her. How much money does each person have respectively?
- Japheth?
- Jaslyn?
|
Case 1 |
Case 2 |
|
Japheth |
Jaslyn |
Japheth |
Jaslyn |
Before |
7 u - 10 |
1 u + 10 |
4 u + 12 |
4 u - 12 |
Change |
+ 10 |
- 10 |
- 12 |
+ 12 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Jaslyn gives Japheth some money or Japheth gives Jaslyn some money, the total amount of money remains the same.
Total amount that Japheth and Jaslyn have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Japheth and Jaslyn each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Japheth has at first in Case 1 and Case 2 is the same.
7 u - 10 = 4 u + 12
7 u - 4 u = 12 + 10
1 u = 22
Amount that Japheth has
= 4 u + 12
= 4 x 22 + 12
= 88 + 12
= $100
(b)
Amount that Jaslyn has
= 1 u + 10
= 22 + 10
= $32
Answer(s): (a) $100; (b) $32