Question

Alex is 12 years older than George. Carl is three times older than Alex The sum of their ages is 68

find the ratio of George's age to Carl's age to Alex's age.​​

Answer 1

1:12:4

Explanation:

Let's say that George's age is x. That means that Alex's age would be x+12

Since Carl is 3 times older, Carl would be 3(x+12)

We put all those in the equation and get this:

x+ x+12 + 3(x+12)=68

2x+12+3x+36=68

5x+48=68

5x=20

x=4

George is 4 years old, Alex is 16, and Carl is 48

Divide every age by 4 to find the ratio

In order of George, Carl, and Alex:

1:12:4

Answer 2

1 : 12 : 4.

Explanation:

Let's start by assigning some variables to the names! We can use a to represent Alex, g to represent George, and c to represent Carl.

Alex is 12 years older than George, which means that a = g + 12.

Carl is three times older than Alex, which means that c = 3a.

The sum of the ages is 68, meaning that a + g + c = 68.

Since c = 3a, we can say that c = 3(g + 12), and that c = 3g + 36.

That way, we can put it all together...

(g + 12) + g + (3g + 36) = 68

g + g + 3g + 12 + 36 = 68

5g + 48 = 68

5g = 20

g = 4

Now that we have George's age, we can calculate the others!

a = g + 12

a = 4 + 12

a = 16

Now that we have Alex's age, we can calculate Carl's!

c = 3a

c = 3 * 16

c = 48

To check out work, 4 + 16 + 48 = 20 + 48 = 68. 4 + 12 = 16. 16 * 3 = 48. It all matches up!

The question asks for the ratio of George's age to Carl's to Alex's, so we can just find the ratio of g : c : a.

4 : 48 : 16

To simplify, divide all three numbers by 4.

1 : 12 : 4.

You can no longer simplify, so there is your answer!

Hope this helps!