Question

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?

Answer 1

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