SOLUTION: Mary is 3 years older than her brother Tom, and Tom is 4 years older than John. Three years ago Mary was twice as old as John. How old is each now?

Question 517531: Mary is 3 years older than her brother Tom, and Tom is 4 years older than John. Three years ago Mary was twice as old as John. How old is each now?
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Present age of Tom = t
Present age of John = j
Present age of Mary =m
Mary is 3 years older than her brother Tom
m=t+3............(1)
Tom is 4 years older than John
t=j+4.............(2)
Three years ago Mary's age was (m-3) and John was (j-3)
Then Mary was twice as old as John
m-3=2(j-3)
m-3=2j-6
m=2j-6+3
m=2j-3.............(3)
We have three equations and three unknowns (m,t,j) and we can solve these equation either by substitution method or elimination method
m=t+3............(1)
t=j+4.............(2)
m=2j-3.............(3)
Put the value of m from (1) to (3)
t+3=2j-3
t=2j-3-3
t=2j-6...............(4)
Put the value of t from (2) to (4)
j+4=2j-6
j-2j=-6-4
-j=-10
Multiply by -1 both sides of above equation
j=10
Put the value of j in (2)
t=j+4
t=10+4
t=14
Put the value of t in (1)
m=t+3............(1)
m=14+3
m=17

Present age of Tom = t = 14 years old
Present age of John = j = 10 years old
Present age of Mary =m = 17 years old

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