on page 50 of algebra woth pizzazz Andy is twice as old as kate. in 6 years, their ages will total 60. How old is each now?
To solve this problem, we'll need to use algebraic equations. Let's break it down step-by-step:
1. Let's assume Kate's current age is "x" years old.
2. According to the problem, Andy is currently twice as old as Kate, so Andy's current age is "2x" years old.
Now, let's move on to the next piece of information:
3. In 6 years, their ages will total 60. This means that we need to add 6 years to both Kate and Andy's ages and get a total of 60. Using our assumptions from steps 1 and 2, we can set up the equation:
(x + 6) + (2x + 6) = 60
4. Now, we can solve the equation for "x." Let's simplify it:
x + 6 + 2x + 6 = 60
3x + 12 = 60
5. Subtract 12 from both sides of the equation:
3x = 60 - 12
3x = 48
6. Divide both sides of the equation by 3:
x = 48 / 3
x = 16
Now we have found Kate's current age (x = 16). To find Andy's current age (2x), we simply multiply 16 by 2:
2x = 2 * 16 = 32
Therefore, Kate is currently 16 years old, and Andy is currently 32 years old.
k = Kate's age
k + 2k + 6 = 60
3k = 54
k = 18