Answer:
The ratio of George age to Carl's age is 1:12.
Step-by-step explanation:
Let the age of George be 'g'.
Let the age of Alex be 'a'.
Also Let the age of Carl be 'c'.
Given:
The sum of their ages is 68.
So equation can be framed as;
[tex]g+a+c=68 \ \ \ \ equation 1[/tex]
Also Given:
Alex is 12 years older than George.
So equation can be framed as;
[tex]a =g+12 \ \ \ \ equation \ 2[/tex]
Now Given:
Carl is three times older than Alex.
[tex]c=3a[/tex]
But [tex]a =g+12[/tex]
So we get;
[tex]c = 3(g+12) \\\\c= 3g+36 \ \ \ \ equation \ 3[/tex]
Now Substituting equation 2 and equation 3 in equation 1 we get;
[tex]g+a+c=68\\\\g+g+12+3g+36=68\\\\5g+48=68[/tex]
Subtracting both side by 48 using subtraction property of equality we get;
[tex]5g+48-48=68-48\\\\5g=20[/tex]
Now Dividing both side by 5 using Division property of equality we get;
[tex]\frac{5g}{5}=\frac{20}{5}\\\\g =4[/tex]
Hence George age [tex]g = 4 \ years[/tex]
Now Alex age [tex]a=g+12 = 4+12 =16\ years[/tex]
Also Carl's age [tex]c=3g+36=3\times 4+36 =12+36 =48\ years[/tex]
Now we need to find the ratio of George age to Carl's age.
[tex]\frac{g}{c}=\frac{4}{48} = \frac{1}{12}[/tex]
Hence the ratio of George age to Carl's age is 1:12.
