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The sum of the ages of a mother and daughter is 39. The mother is 3 years younger than the square of the daughter's age. How old is the mother and daughter?

Sagot :

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From the given information:

1. The sum of their ages is 39: x + y = 39

2. The mother is 3 years younger than the square of the daughter's age: y = x^2 - 3

Now, we can substitute the second equation into the first equation:

x + (x^2 - 3) = 39

x + x^2 - 3 = 39

x^2 + x - 3 = 39

x^2 + x - 42 = 0

Now, we can solve this quadratic equation to find the values of x (daughter's age). By solving this equation, we find:

x = 6 or x = -7

Since age cannot be negative, the daughter's age is 6 years old. Now, we can substitute x back into the second equation to find the mother's age:

y = 6^2 - 3

y = 36 - 3

y = 33

Therefore, the daughter is 6 years old, and the mother is 33 years old.

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