Michael and Jenson have some money. If Michael gives $141 to Jenson, the ratio of their money will be 2 : 5. If Michael gives $690 to Jenson, the ratio of their money will be 1: 4. How much does Michael have?
| |
Case 1 |
Case 2 |
| |
Michael |
Jenson |
Michael |
Jenson |
| Before |
10 u + $141 |
25 u - $141 |
7 u + $690 |
28 u - $690 |
| Change |
- $141 |
+ $141 |
- $690 |
+ $690 |
After
|
2x5 =
10 u |
5x5 =
25 u |
1x7 =
7 u |
4x7 =
28 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 7 and 5 is 35.
The amount that Michael has at first is the same in both cases.
10 u + 141 = 7 u + 690
10 u - 7 u = 690 - 141
3 u = 549
1 u = 549 ÷ 3 = 183
Amount that Michael has
= 10 u + 141
= 10 x 183 + 141
= 1830 + 141
= $1971
Answer(s): $1971
