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joey and chloe and their daughter zoe all have the same birthday. joey is 11 year older than chloe, and zoe is exactly 11 year old today. today is the first of the 99 birthdays on which chloe's age will be an integral multiple of zoe's age. what will be the sum of the two digits of joey's age the next time his age is a multiple of zoe's age?



Answer :

The sum of the two digits of Joey's age the next time his age is a multiple of Zoe's age is of 11, and this measure was found using a system of equations.

What is the system of equations?

The variables for the system of equations in this problem are given as follows:

  • Variable x: Joey's age.
  • Variable y: Chloe's age.
  • Variable z: Zoe's age.

Joey is one year older than Chloe, hence:

x = y + 1.

Zoe is exactly one year old, hence:

z = 1.

The difference between the ages of Chloe's and Zoe's have 9 factors. Numbers with nine factors have the following format:

x² x y² , with different x and y.

These numbers have to be different of 1, due to Zoe's age, hence the smallest number is given as follows:

2² x 3² = 4 x 9 = 36.

Since the difference is of 36 years old, so the ages are as follows:

  • Zoe: 1 year old.
  • Chloe: 37 years old.
  • Joey: 38 years old.

The next time this will happen is in 36 years, hence Joey's age will be of:

36 + 38 = 74 years old.

The sum of the digits will be of:

7 + 4 = 11.

More can be learned about a system of equations at https://brainly.com/question/24342899

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