Question 562871: Sue is twice as old as Emma and 7 years older than Abby. The sum of their ages is 53. How old is each? Found 2 solutions by josmiceli, Maths68:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Let = Sue's age
Let = Emma's age
Let = Abby's age
given:
(1)
(2)
(3)
This is 3 equations and 3 unknowns,
so it's solvable
---------------
(2)
(2)
and
(1)
Substitute (1) and (2) into (3)
(3)
(3)
(3)
(3)
(3)
and
(2)
(2)
(2)
and
(1)
(1)
(1)
Sue's age is 24
Emma's age is 12
Abby's age is 17
check:
(3)
(3)
OK
You can put this solution on YOUR website! Let
Present age of Sue = s
Present age of Emma = e
Present age of Abby = a
Given
Sue is twice as old as Emma
s=2e
s/2=e
e=s/2.........(1)
and 7 years older than Abby
s=a+7
s-7=a
a=s-7........(2)
The sum of their ages is 53
a+e+s=53.......(3)
We have three unknowns and three equations.
Put the values of e and a from (1) and (2) to (3)
a+e+s=53.......(3)
s-7+s/2+s=53
Multiply by 2 both sides of the equation
2s-14+s+2s=106
5s-14=106
5s=106+14
5s=120
5s/5=120/5
s=24
Put the value of s in (1)
e=s/2.........(1)
e=24/2
e=12
Put the value of s in (2)
a=s-7........(2)
a=24-7
a=17
Present age of Sue = s = 24 years old
Present age of Emma = e = 12 years old
Present age of Abby = a = 17 years old
