SOLUTION: Ashley is five years younger than Robert. Carolyn is three times as old as Ashley. William is three times as old as Robert. The sum of their ages is 60. How old is Carolyn?
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Question 517498: Ashley is five years younger than Robert. Carolyn is three times as old as Ashley. William is three times as old as Robert. The sum of their ages is 60. How old is Carolyn? Answer by Maths68(1474) (Show Source):
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Present age of Ashley = a
Present age of Robert = r
Present age of Carolyn = c
Present age of William = w
Ashley is five years younger than Robert.
r=a+5.........(1)
Carolyn is three times as old as Ashley.
c=3a.........(2)
William is three times as old as Robert.
w=3r..........(3)
Put the value of r from (1) to (3)
w=3(a+5)
w=3a+15.......(4)
The sum of their ages is 60.
a+r+c+w=60....(5)
Put the value of r from (1),value of c from (2) and value of w from (4) to (5)
a+r+c+w=60
a+(a+5)+(3a)+(3a+15)=60
a+a+5+3a+3a+15=60
8a+20=60
8a=60-20
8a=40
8a/8=40/8
a=5
Put the value of a in (2)
c=3a
c=3(5)
c=15
Put the value of a (1)
r=a+5
r=5+5
r=10
Put the value of a in (4)
w=3a+15
w=3(5)+15
w=15+15
w=30
Present age of Ashley = a = 5 years old
Present age of Robert = r = 10 years old
Present age of Carolyn = c = 15 years old
Present age of William = w = 30 years old
