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?

Step-by-step explanation:

Let the age of Juan be x

Let the age of Gabe be y

Let the age of catherine be z

The sum of their ages is 149, then;

x+y+z = 149

If Juan is three times as old as Gabe, then;

x = 3y 2

If Gabe is six years older than Catherine, then;

y = z + 6

z = y-6 3

Substitute 2 and 3 into 1;

From 1; x+y+z = 149

3y+y+y-6 = 149

5y = 149+6

5y = 155

y = 31

Since x = 3y

x = 3*31

x = 93

If z = y-6

z = 31-6

z = 25

Hence Juan is 93 years old

Gabe is 31 years old

Catherine is 25 years old