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

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) (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) (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:
------ 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.
RELATED QUESTIONS
When ralph asked his math teacher how old she was, she answered: Ten years ago, my age... (answered by ikleyn)
When joe was 11 years old, he asked his uncle: how old are you?. His uncle answered: I... (answered by ankor@dixie-net.com)
Jesse asks his math teacher her age and her husband's age. Jesse's teacher responds that... (answered by ikleyn)
Today my daughter is 1/3 of my age. Five years ago she was 1/4 of my age then. How... (answered by solver91311)
Kevin was asked how old he is. He answered "if you tripple my age in teo years' time, it... (answered by htmentor)
Anna made the following announcement: " In 7 years, I will be half my mother's age.... (answered by Alan3354)
The math teacher asked Edith, " how old are you?" Sixty years less than five time my... (answered by swincher4391)
a movie star unwilling to give his age posed the following riddle seven years ago i... (answered by josmiceli)
One more Q: Sarah went to get her drivers license. When asked her age, she replied " my... (answered by ikleyn)