Tim and Asher have some money. If Tim gives $184 to Asher, the ratio of their money will be 2 : 5. If Tim gives $553 to Asher, the ratio of their money will be 1: 4. How much does Tim have?
| |
Case 1 |
Case 2 |
| |
Tim |
Asher |
Tim |
Asher |
| Before |
10 u + $184 |
25 u - $184 |
7 u + $553 |
28 u - $553 |
| Change |
- $184 |
+ $184 |
- $553 |
+ $553 |
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 Tim has at first is the same in both cases.
10 u + 184 = 7 u + 553
10 u - 7 u = 553 - 184
3 u = 369
1 u = 369 ÷ 3 = 123
Amount that Tim has
= 10 u + 184
= 10 x 123 + 184
= 1230 + 184
= $1414
Answer(s): $1414
