Question

The sum of the age of mother and daughter is 68. If the mother is four less than the square of the daughter's age, how old are they?

A) Mother: 48, Daughter: 20
B) Mother: 47, Daughter: 21
C) Mother: 44, Daughter: 24
D) Mother: 45, Daughter: 23

Answer 1

To find the ages of the mother and daughter, we can set up a quadratic equation by using the given information and then solve for the variables.the correct answer is D) Mother: 45, Daughter: 23.

Step-by-step explanation:

Let's represent the daughter's age as x.

The mother's age is four less than the square of the daughter's age, so the mother's age can be represented as (x^2) - 4.

The sum of their ages is 68, so we can write the equation: x + (x^2) - 4 = 68.

Combining like terms and setting the equation equal to zero gives us the quadratic equation: (x^2) + x - 64 = 0.

Using factoring or the quadratic formula, we find that the daughter's age is 8 and the mother's age is 60.

Therefore, the correct answer is D) Mother: 45, Daughter: 23.