Question

B: Alex is 12 years older than George.

Answer 1

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;

$g+a+c=68 \ \ \ \ equation 1$

Also Given:

Alex is 12 years older than George.

So equation can be framed as;

$a =g+12 \ \ \ \ equation \ 2$

Now Given:

Carl is three times older than Alex.

$c=3a$

But $a =g+12$

So we get;

$c = 3(g+12) \\\\c= 3g+36 \ \ \ \ equation \ 3$

Now Substituting equation 2 and equation 3 in equation 1 we get;

$g+a+c=68\\\\g+g+12+3g+36=68\\\\5g+48=68$

Subtracting both side by 48 using subtraction property of equality we get;

$5g+48-48=68-48\\\\5g=20$

Now Dividing both side by 5 using Division property of equality we get;

$\frac{5g}{5}=\frac{20}{5}\\\\g =4$

Hence George age $g = 4 \ years$

Now Alex age $a=g+12 = 4+12 =16\ years$

Also Carl's age $c=3g+36=3\times 4+36 =12+36 =48\ years$

Now we need to find the ratio of George age to Carl's age.

$\frac{g}{c}=\frac{4}{48} = \frac{1}{12}$

Hence  the ratio of George age to Carl's age is 1:12.