Last year, Ben was 4 times as old as his son, Seth. This year, their total age is 112 years old. How old will Ben be when he is 3 times as old as Seth?
| |
Ben |
Seth |
Difference |
Total |
| Before |
4x2 =
8 u |
1x2 =
2 u |
3x2 =
6 u |
|
| Change 1 |
+ 1 |
+ 1 |
|
|
| After 1 |
8 u + 1 |
2 u + 1 |
|
112 |
| Change |
+ ? |
+ ? |
|
|
After 2 |
3x3 =
9 u |
1x3 =
3 u |
2x3 =
6 u |
|
The difference in Ben's age and his son's age always remains unchanged. Make the difference in age the same. LCM of 3 and 2 is 6.
Total age of Ben and his son this year
= 8 u + 1 + 2 u + 1
= 10 u + 2
10 u + 2 = 112
10 u = 112 - 2
10 u = 110
1 u = 110 ÷ 10 = 11
Ben's age when he is 3 times as old as Seth
= 9 u
= 9 x 11
= 99
Answer(s): 99
