SOLUTION: One day in math class Mia invented a problem for her classmates to solve. She said, �My mom�s and dad�s ages are 3 years apart. I�m exactly 1/4 of my mom�s age, and I�m 24 years yo

Question 999273: One day in math class Mia invented a problem for her classmates to solve. She said, �My mom�s and dad�s ages are 3 years apart. I�m exactly 1/4 of my mom�s age, and I�m 24 years younger than Dad. How old am I?�
Mia was surprised when her classmates came up with two different ages that fit her clues.
What answers did her classmates find?
Explain how you solved the problem. Show how you know both answers are correct.
Extra: Suppose that Mia is 1/3 of her mother's age. Find two other numbers to replace the differences of 3 and 24 that still result in two possible ages for Mia.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
x, Mother
y, Father
m, Mia

This equating formulas for m gives a simpler system

A minor simplification gives

Substitution:

and concentrate on solving for Father's age, y. Use this result to evaluate Mia's age.

This solution posting will stop here but you should, and probably can continue.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

One day in math class Mia invented a problem for her classmates to solve. She said, �My mom�s and dad�s ages are 3 years apart. I�m exactly 1/4 of my mom�s age, and I�m 24 years younger than Dad. How old am I?�
Mia was surprised when her classmates came up with two different ages that fit her clues.
What answers did her classmates find?
Explain how you solved the problem. Show how you know both answers are correct.
Extra: Suppose that Mia is 1/3 of her mother's age. Find two other numbers to replace the differences of 3 and 24 that still result in two possible ages for Mia.

They found that Mia could be: years old, considering that dad is older than mom, but that Mia could also be: years old, considering that mom is older than dad.
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