SOLUTION: Carol is three times as old as John who is ten years older than Henry. The sum of their ages is 140 years. Calculate their ages.

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Question 1024911: Carol is three times as old as John who is ten years older than Henry. The sum of their ages is 140 years. Calculate their ages.
Found 2 solutions by ikleyn, Timnewman:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
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Carol is three times as old as John who is ten years older than Henry. The sum of their ages is 140 years. Calculate their ages.
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C = 3J,           (1)     ("Carol is three times as old as John")
J = H + 10,       (2)     ("John . . . is ten years older than Henry")
C + J + H = 140.  (3)     ("The sum of their ages is 140 years")


Substitute (1) and (2) into (3). You will get

3J + (H + 10) + H = 140.   (4)

Substitute (2) into (4). You will get a single equation for H:

3*(H+10) + (H+10) + H = 140.

Simplify and solve it for H:

3H + 30 + H + 10 + H = 40,
5H = 140 - 30 - 10 = 100,

H =  = 20.  It is Henry's age.

Then John is J = H + 10 = 20 + 10 = 30 years,  and
C = 3J = 3*30 = 90 years for Carol.


Answer by Timnewman(323)   (Show Source): You can put this solution on YOUR website!
let henry's age be x,
John's age =10+x
Carol's age=3(10+x)=30+3x
but the sum of their ages is 140yrs,
Then,
x+30+3x+10+x=140
5x+40=140
5x=140-40
5x=100
x=20
hary's age is 20yrs
carol's age is 30+3(20)=90yrs
John;s age=10+20=30yrs
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