SOLUTION: The sum of the ages of a mother and her son is 26 years. Five years hence, the mother's age will be five times the son's age. what are their present ages?

Question 598275: The sum of the ages of a mother and her son is 26 years. Five years hence, the mother's age will be five times the son's age. what are their present ages?
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
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[I] Define your variables.
Let m be the mother's present age.
Let s be the son's present age.
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[II] Write equations showing the given relationships.
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The phrase, "the sum of the ages of the mother and her son," can be written as m+s. The sum is 26, so

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The phrase, "five years hence, the mother's age" or "five years from now, the mother's age" can be written as m+5. For the son, it would be s+5. Since the mother's age will be five times the son's age, the equation is

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Simplify this equation.

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[III] Solve the system of equations for m and s.
Rewrite the first equation in terms of m.

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Substitute 26-s for m in the second equation.

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Simplify and solve for s.

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The equation s=1 means that the son's current age is 1 year old. The sum of their ages is 26, so the mother is 26-1=25 years old.
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[IV] Check your work
How old will the mother be five years hence? 25+5=30 years old
How old will the son be? 1+5=6 years old
Will the mother be five times as old as the son? 6*5=30...YES!
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Their present ages are 1 and 25 years.
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That's it! Feel free to email if the solution is unclear.
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Ms.Figgy
math.in.the.vortex@gmail.com
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