Juan is three times as old as Gabe and Gabe is six years older than Catherine. If the sum of their ages is 149, how old is each person? Define a variable, write an equation, solve the equation, and answer in a complete sentence.

Juan = 93 years.

Gabe = 31 years.

Catherine = 25 years.

Step-by-step explanation:

Let the age of Juan = J

Let the age of Gabe = G

Let the age of Catherine = C

Translating the word problem into an algebraic equation, we have;

..........equation 1

........equation 2

........equation 3

We would solve the linear equations by using the substitution method;

Substituting equation 2 into equation 1;

........equation 4

Substituting equation 2 and equation 4 into equation 3;

Simplifying the equation, we have;

C = 25 years.

To find G; from equation 2

Substituting the value of "C" into equation 2, we have;

G = 31 years.

To find J; from equation 1

Substituting the value of "G" into equation 1, we have;

J = 93 years.

Therefore, Juan is 93 years old, Gabe is 31 years old and Catherine is 25 years old.