Juan is three times as old as carmen. together their ages add up to 24. how old is each?

Carmen is 6 and jaun is 18 because 6. Times 3 equals 18 and if you add 6 to 18 you will get 24

You could solve it with this equation;  3x + x = 24
Let 3x = Juan's age
let x = Carmen's age
Now lets solve their ages!

3x + x = 24
4x = 24 (combined liked terms)
x = 24 ÷ 4 
x = 6
So Carmen's age is...6

Now lets substitute the value of x in the original equation to find Juan's age;

3x + x = 24
3(6) + (6) = 24
(3 × 6)+ 6 = 24
(18) + 6 = 24
24 = 24
So Juan's age is...18

Lets check if their ages add up to 24;
18 + 6 = 24 
24 = 24
So their ages are correct! Hope this helps you! :D