Question 793770: Noel is 3 times as old as Sachi. He is 5 years older than Eiko. The sum of all their ages is 30. How old is each?
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! n for Noel
s for Sachi
e for Eiko.
n=3s. n=5+e. n+s+e=30. Three equations in three unknowns.
First, equation the n expressions: 3s=5+e.
Next, substitute n=5+e into the age sum equation: 5+e+s+e=30, and simplify this.
2e+s=30-5
2e+s=25.
Back to the first substituted equation, simplify that one a little more:
3s-e=5
-e+3s=5.
Continue with the simpler system in e and s:
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2e+s=25 and -e+3s=5.
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Add twice the second one to the first one and find the value for s:
2e+s+(-2e+6s)=25+10
2e+s-2e+6s=35
7s=35
s=5---------------First Value Found.
Next is easier to find n, from the equation that came in the problem description.
n=3s
n=3*5
n=15 ---------------Second found value.
Let's try now n=5+e,
e=n-5
e=15-5
e=10 ----------------Third found value.
SUMMARY:
Noel is 15, Sachi is 5, Eiko is 10.
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