If Japheth gives Dana $9, he will have the same amount of money as her. If Dana gives Japheth $9, Japheth will have five times as much money as her. How much money does Dana have?
| |
Scenario 1 |
Scenario 2 |
| |
Japheth |
Dana |
Total |
Japheth |
Dana |
Total |
| Before |
3 u + 9 |
3 u - 9 |
|
1 u - 9 |
5 u + 9 |
|
| Change |
- 9 |
+ 9 |
|
+ 9 |
- 9 |
|
| After |
1x3 =
3 u |
1x3 =
3 u |
2x3 =
6 u |
1x1 =
1 u |
5x1 =
5 u |
6x1 =
6 u |
The total amount in both scenarios is the same. LCM of 2 and 6 is 6.
In both scenarios, Japheth had the same amount at first.
3 u + 9 = 1 u - 9
3 u - 1 u = 9 + 9
2 u = 18
1 u = 18 ÷ 2 = 9
Amount that Dana has
= 3 u - 9
= 3 x 9 - 9
= $18
Answer(s): $18
