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--
.
[I] Define your variables.
Let m be the mother's present age.
Let s be the son's present age.
.
.
[II] Write equations showing the given relationships.
.
The phrase, "the sum of the ages of the mother and her son," can be written as m+s. The sum is 26, so
.
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
.
Simplify this equation.
.
.
[III] Solve the system of equations for m and s.
Rewrite the first equation in terms of m.
.
Substitute 26-s for m in the second equation.
.
Simplify and solve for s.
.
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.
.
.
[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!
.
Their present ages are 1 and 25 years.
.
That's it! Feel free to email if the solution is unclear.
.
Ms.Figgy
math.in.the.vortex@gmail.com
|
|
|
