katie is k years old. harry is 4 years older than katie. rachel is twice as old as harry. if you add together the ages of katie, harry, and rachel the total comes to 36 years. algebraically, determine the age of each person

k +(k+4) + 2(k+4) = 36

4 k + 12 = 36

4 k = 24

now you finish

k=24/4

k=6

To determine the age of each person algebraically, let's assign variables:

Let's say Katie's age is represented by "k".
Harry's age is 4 years older than Katie's, so his age can be represented as "k + 4".
Rachel's age is twice as old as Harry's, so her age can be represented as "2(k + 4)".

According to the information given, the sum of their ages is 36, so we can set up the equation:

k + (k + 4) + 2(k + 4) = 36

Now, let's simplify the equation and solve for k:

k + k + 4 + 2k + 8 = 36
4k + 12 = 36
4k = 36 - 12
4k = 24

To isolate "k," we can divide both sides of the equation by 4:

4k / 4 = 24 / 4
k = 6

So, Katie's age is 6 years old.

Now, let's substitute the value of k into the expressions for Harry and Rachel's ages:

Harry's age = k + 4 = 6 + 4 = 10 years old
Rachel's age = 2(k + 4) = 2(6 + 4) = 2(10) = 20 years old

Therefore, Katie is 6 years old, Harry is 10 years old, and Rachel is 20 years old.