Tom and Mark have some money. If Tom gives $147 to Mark, the ratio of their money will be 2 : 5. If Tom gives $630 to Mark, the ratio of their money will be 1: 4. How much does Tom have?
|
Case 1 |
Case 2 |
|
Tom |
Mark |
Tom |
Mark |
Before |
10 u + $147 |
25 u - $147 |
7 u + $630 |
28 u - $630 |
Change |
- $147 |
+ $147 |
- $630 |
+ $630 |
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 Tom has at first is the same in both cases.
10 u + 147 = 7 u + 630
10 u - 7 u = 630 - 147
3 u = 483
1 u = 483 ÷ 3 = 161
Amount that Tom has
= 10 u + 147
= 10 x 161 + 147
= 1610 + 147
= $1757
Answer(s): $1757