Reggie and Lee have some money. If Reggie gives $142 to Lee, the ratio of their money will be 2 : 5. If Reggie gives $643 to Lee, the ratio of their money will be 1: 4. How much does Reggie have?
| |
Case 1 |
Case 2 |
| |
Reggie |
Lee |
Reggie |
Lee |
| Before |
10 u + $142 |
25 u - $142 |
7 u + $643 |
28 u - $643 |
| Change |
- $142 |
+ $142 |
- $643 |
+ $643 |
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 Reggie has at first is the same in both cases.
10 u + 142 = 7 u + 643
10 u - 7 u = 643 - 142
3 u = 501
1 u = 501 ÷ 3 = 167
Amount that Reggie has
= 10 u + 142
= 10 x 167 + 142
= 1670 + 142
= $1812
Answer(s): $1812
