Last year, Archie was 3 times as old as his son, Eric. This year, their total age is 54 years old. How old will Archie be when he is 2 times as old as Eric?
| |
Archie |
Eric |
Difference |
Total |
| Before |
3x1 =
3 u |
1x1 =
1 u |
2x1 =
2 u |
|
| Change 1 |
+ 1 |
+ 1 |
|
|
| After 1 |
3 u + 1 |
1 u + 1 |
|
54 |
| Change |
+ ? |
+ ? |
|
|
After 2 |
2x2 =
4 u |
1x2 =
2 u |
1x2 =
2 u |
|
The difference in Ben's age and his son's age always remains unchanged. Make the difference in age the same. LCM of 2 and 1 is 2.
Total age of Archie and his son this year
= 3 u + 1 + 1 u + 1
= 4 u + 2
4 u + 2 = 54
4 u = 54 - 2
4 u = 52
1 u = 52 ÷ 4 = 13
Archie's age when he is 2 times as old as Eric
= 4 u
= 4 x 13
= 52
Answer(s): 52
