SOLUTION: Jeanne is three times as old as Michel. The sum of their ages is 20 years. Find out their age now.

Question 72347: Jeanne is three times as old as Michel. The sum of their ages is 20 years. Find out their age now.
Found 2 solutions by bucky, Earlsdon:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Call Jeanne's age J and call Michael's age M.
.
The problem tells you that Jeanne is 3 times Michael's age. In equation form this is:
.
J = 3*M
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The problem also tells you that the sum of their ages is 20. In equation form this is:
.
J + M = 20
.
There are two unknowns and therefore we need two equations to solve for these unknowns.
We have our two equations.
.
As a result of our first equation we known that J = 3*M. Therefore, we can substitute
3*M for J in our second equation. When we do that the second equation becomes:
.
3*M = M = 20
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Adding the terms on the left side results in:
.
4*M = 20
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Dividing both sides of this equation by 4 tells us that:
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M = 5
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So we know that Michael's age is 5. And since Jeanne is 3 times as old as Michael,
then Jeanne must be 15.
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Finally, as a check, you can note that the sum of their ages (5 + 15) is 20, which is
exactly what the problem said it should be.
.
Hope this helps you to understand how to translate this word problem into equations,
and then how to solve the equations to get the answer.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let J = Jeanne's age and M = Michel's age. From the problem description, you can write:
J = 3M Substitute this into the equation below and solve for M
J + M = 20
3M + M = 20
4M = 20 Divide both sides by 4.
M = 5 This is Michels's age.
J = 3M = 3(5) = 15 This is Jeanne's age.
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