SOLUTION: Mary is twice as old as Jane was when Mary was as old as Jane is now. In 3 years Mary will be 3 times as old as Jane was 4 years ago. Find their present ages.

Question 1170858: Mary is twice as old as Jane was when Mary was as old as Jane is now. In 3 years Mary will be 3 times as old as Jane was 4 years ago. Find their present ages.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Mary is twice as old as Jane was when Mary was as old as Jane is now.
let m-j = d, the difference in their ages
m = 2(j - d)
m = 2j - 2d
replace d with m-j
m = 2j - 2(m-j)
m = 2j - 2m + 2j
m = 4j - 2m
m + 2m = 4j
3m = 4j
:
In 3 years Mary will be 3 times as old as Jane was 4 years ago.
m + 3 = 3(j-4)
m + 3 = 3j - 12
m = 3j - 12 - 3
m = 3j - 15
:
in the first equation, replace m with (3j-15)
3(3j - 15) = 4j
9j - 45 = 4j
9j - 4j = 45
5j = 45
j = 45/5
j = 9 yrs is Jane's age
then
m = 3j - 15
m = 3(9) - 15
m = 12 yrs is Mary's age

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