I don't get page 50 of algebra with pizzazz!

Please help?
7) Kathy is 6 years younger than bill. 12 years ago bill was twice as old as Kathy was then. How old are they now?

let Bill's present age be x

then Kathy's present age is x-6

12 years ago:
Bill was x-12
Kathy was x-6 - 12 or x - 18

at that time bill was twice as old as Kathy --- x-12 = 2(x-18)

x-12 = 2x - 36
-x = -24
x = 24

so now bill is 24 and Kathy is 18

Alright thanks I get it now (:

I guess I was just multiplying wrong.

To solve this problem, let's use algebraic equations.

Let's assume Kathy's current age is "K" and Bill's current age is "B".

We are given two pieces of information:

1) Kathy is 6 years younger than Bill. This can be represented as:
K = B - 6

2) 12 years ago, Bill was twice as old as Kathy was then. This can be represented as:
B - 12 = 2(K - 12)

Now, we can solve the system of equations to find the ages of Kathy and Bill.

Substituting the value of K from the first equation into the second equation, we get:
B - 12 = 2((B - 6) - 12)

Next, simplify the equation:
B - 12 = 2(B - 18)

Expanding and simplifying further:
B - 12 = 2B - 36

Moving all the variables to one side of the equation:
B - 2B = -36 + 12
-B = -24

Dividing both sides by -1:
B = 24

Now that we have found Bill's age, we can substitute this value back into the first equation to find Kathy's age.
K = B - 6 = 24 - 6 = 18

Therefore, Bill is currently 24 years old and Kathy is currently 18 years old.

To understand page 50 of Algebra with Pizzazz, we need to solve the problem given in question 7.

Let's break down the problem step by step:

1) Kathy is 6 years younger than Bill:
Let's assume Bill's age as 'x'. Now, Kathy's age would be 'x - 6' since she is 6 years younger.

2) 12 years ago, Bill was twice as old as Kathy was then:
To solve this, let's subtract 12 from both Bill and Kathy's ages. So, Bill's age now would be 'x - 12' and Kathy's age now would be '(x - 6) - 12'. According to the problem, Bill's age 12 years ago was twice Kathy's age at that time:
(x - 12) = 2 * [(x - 6) - 12]

Now, let's solve this equation step by step:

(x - 12) = 2 * [(x - 6) - 12]
Expanding the brackets:
(x - 12) = 2 * (x - 6 - 12)
(x - 12) = 2 * (x - 18)
(x - 12) = 2x - 36
x - 2x = -36 + 12
-x = -24
Dividing both sides by -1 (to isolate 'x'):
x = 24

Therefore, we found that Bill's age is 24.

Now, let's find Kathy's age:
Kathy's age = x - 6 = 24 - 6 = 18

So, Bill is 24 years old and Kathy is 18 years old.