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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 :

The12idn

Answer:

The mother is 33 years old, while the daughter is aged 6.

Step-by-step explanation:

  • Interpret the given values into mathematical equations. Let x be the mother's age, and let y be the daughter's age.

"The sum of the ages of a mother and daughter is 39." [Equation 1]
[tex]x+y=39[/tex]

"The mother is 3 years younger than the square of the daughter's age." [Equation 2]
[tex]x=y^2-3[/tex]

  • Since there is an initial value for x, substitute it to equation 1.

[tex]x+y=39\\(y^2-3)+y=39\\y^2+y-3=39\\y^2+y-42=0\\(y+7)(y-6)=0\\\\y=-7 ; y=6[/tex]

  • There is no negative age, hence the daughter's age is 6.
  • To find the mother's age, substitute the daughter's age to any of the two equations.

Via Equation 1:
[tex]x+y=39\\x+6=39\\x=33[/tex]

Via Equation 2:

[tex]x=y^2-3\\x=(6)^2-3\\x=36-3\\x=33[/tex]

  • The mother's age is 33. You may try substituting the values of x and y to Equations 1 & 2 to verify if the solutions of the equations are correct.
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