Answer:
Joe's age is 93 years
Aaron's age is 31 years
Christina's age is 25 years
Step-by-step explanation:
Let
x ---->Joe's age
y ----> Aaron's age
z----> Christina's age
we know that
Joe"s Age Is three times Aaron's age
[tex]x=3y[/tex] ----> equation A
Aaron is six years older than Christina
[tex]y=z+6[/tex]
isolate the variable z
[tex]z=y-6[/tex] ----> equation B
The sum of their ages is 149
[tex]x+y+z=149[/tex] ----> equation C
solve the system by substitution
substitute equation A and equation B in equation C
[tex](3y)+y+(y-6)=149[/tex]
solve for y
Combine like terms left side
[tex]5y-6=149[/tex]
Adds 6 both sides
[tex]5y=149+6[/tex]
[tex]5y=155[/tex]
Divide by 5 both sides
[tex]y=31[/tex]
Find the value of x
[tex]x=3y[/tex] ----> [tex]x=3(31)=93[/tex]
Find the value of z
[tex]z=y-6[/tex] ---- [tex]z=31-6=25[/tex]
therefore
Joe's age is 93 years
Aaron's age is 31 years
Christina's age is 25 years
