Japheth and Lynn has some money each. If Lynn gives Japheth $19, he will have 7 times as much money as her. If Japheth gives Lynn $18, he will have the same amount of money as her. How much money does each person have respectively?
- Japheth?
- Lynn?
| |
Case 1 |
Case 2 |
| |
Japheth |
Lynn |
Japheth |
Lynn |
| Before |
7 u - 19 |
1 u + 19 |
4 u + 18 |
4 u - 18 |
| Change |
+ 19 |
- 19 |
- 18 |
+ 18 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Lynn gives Japheth some money or Japheth gives Lynn some money, the total amount of money remains the same.
Total amount that Japheth and Lynn have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Japheth and Lynn 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 - 19 = 4 u + 18
7 u - 4 u = 18 + 19
1 u = 37
Amount that Japheth has
= 4 u + 18
= 4 x 37 + 18
= 148 + 18
= $166
(b)
Amount that Lynn has
= 1 u + 19
= 37 + 19
= $56
Answer(s): (a) $166; (b) $56
