SOLUTION: When Ralph asked his math teacher how old she was, she answered: "Ten years ago, my age was equal to the square of my daughter's age. In 14 years, I will be twice as old as my daug

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Question 1159096: When Ralph asked his math teacher how old she was, she answered: "Ten years ago, my age was equal to the square of my daughter's age. In 14 years, I will be twice as old as my daughter."What is the age of math Teacher
Found 2 solutions by VFBundy, MathTherapy:
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Teacher's age = x
Daughter's age = y

x - 10 = (y - 10)²
x + 14 = 2(y + 14)

x - 10 = y² - 20y + 100
x + 14 = 2y + 28

x = y² - 20y + 110
x = 2y + 14

y² - 20y + 110 = 2y + 14

y² - 22y + 96 = 0

y = 6; y = 16

So the daughter's age (y) can be either 6 or 16. Plug y = 6 into:

x - 10 = (y - 10)²

x - 10 = (6 - 10)²

x - 10 = (-4)²

x - 10 = 16

x = 26

So, we know that one solution is that the teacher is 26 and her daughter is 6.

Plug y = 16 into:

x - 10 = (y - 10)²

x - 10 = (16 - 10)²

x - 10 = (6)²

x - 10 = 36

x = 46

Another solution is that the teacher is 46 and her daughter is 16. This is probably the answer they are looking for.

Each solution DOES technically work, but when the teacher is 26 and her daughter is 6, the statement "Ten years ago, my age was equal to the square of my daughter's age," would involve subtracting 10 years from the daughter's age of 6 and making her be -4 years old. The math still works, but would you ever consider someone who was 6 years old to be -4 years old 10 years ago?

Anyway...the safe answer is that the teacher is 46.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
When Ralph asked his math teacher how old she was, she answered: "Ten years ago, my age was equal to the square of my daughter's age. In 14 years, I will be twice as old as my daughter."What is the age of math Teacher
Let teacher's and daughter's ages be T, and D, respectively

Then we get:  

matrix%281%2C3%2C+2D+%2B+14+-+10%2C+%22=%22%2C+%28D+-+10%29%5E2%29 ------ Substituting 2D + 14 for T in eq (i)



(D - 6)(D - 16) = 0

D - 6 = 0       OR        D - 16 = 0

D = 6           OR        D = 16

Daughter's age CANNOT be 6 because 10 years ago she was alive. 

Therefore, daughter is 16 years-old.

Substitute this value into eq (ii) to find teacher's age.