SOLUTION: Jack is 2 times as old as Lacy. 6 years ago the sum of their ages was 24. How old are they now?

Question 760442: Jack is 2 times as old as Lacy. 6 years ago the sum of their ages was 24. How old are they now?
Answer by aquacean(7) (Show Source): You can put this solution on YOUR website!
I have two methods: a.) the "scratchpad" method (no use of algebra really) and b.) the "orthodox" one (variables, systems and all that)

A. Scratchpad method
6*2=12
24+12=36
36/3=12
12*2=24
12 = Lacy's age
24 = Jack's age
I multipied 6(years ago) by 2 because they are two persons, thus each year is always multiplied by how many persons involved.
Then I added the 12 to 24 to find the total sum of their age at present which is 36. And since Jack is twice as old as Lacy, we divide 36 into 3, 1/3 of 36 is 12 which is Lacy's age and 2/3 of it is 24 which is Jack's age.

B. "Orthodox" Method
a = Lacy's age
2a = Jack's age
Lacy's age:
3a = 24 + 6(2)
a = 36/3
a = 12
Jack's age:
2a = 12(2)
2a = 24

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