Respuesta :
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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