SOLUTION: Sue is twice as old as Emma and 7 years older than Abby. The sum of their ages is 53. How old is each?

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
Answer by Maths68(1474) (Show Source): 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

RELATED QUESTIONS
Sue is twice as old as Emma and 7 years older than Abby. The sum of their ages is 53. How (answered by Alan3354)
Eli's sister Emma is 6 years older than he is. His father is 3 times as old as Emma. The... (answered by algebra hello)
Bob is 8 years older than Sue. 4 years ago, Bob was twice as old as Sue. What is the sum... (answered by josgarithmetic)
Chan is 4 years older than Sue and the sum of their ages 46 how old is... (answered by jorel1380)
Ken is 3 times as old as Emma . Sam is half as old as Emma . The sum of their ages are... (answered by pj66)
john is twice as old as bill. greg is 7 years older than bill. four years ago, the sum of (answered by JBarnum)
Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages (answered by Edwin McCravy)
Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages (answered by Boreal)
Mel is 3 years older than Rafat and Aurelio is twice as old as Mel. The sum of their... (answered by jorel1380)