To solve this problem, we can set up a system of equations. Let's let the variable p represent the number of peanut butter cookies that were sold and the variable c represent the number of chocolate chip cookies that were sold. Using our given information, we know that the number of chocolate chip cookies must be half the number of peanut butter cookies, or 1/2p = c. Because there are 12 cookies in a dozen and twenty dozen cookies were sold total, we know that the sum of the chocolate chip and peanut butter cookies must equal twenty dozen, or p + c = 20(12). So, our system of equations is:
1/2p = c
p + c = 20(12)
To solve, we can substitute the value for c in terms of p given by the first equation into the second equation for the variable c, and then solve for p. This is shown below:
p + c = 20(12)
p + 1/2p = 20(12)
To simplify, we should compute the addition on the left side of the equation and the multiplication on the right side of the equation, which gives us:
1 1/2p = 240
To solve for p, we must get this variable alone. To do this, we should divide both sides of the equation by 1 1/2.
p = 160
Now, we can substitute this value for p into one of our original equations to solve for c:
1/2p = c
1/2(160) = c
To solve, we just multiply the two factors on the left side of the equation together.
c = 80
Therefore, your answer is that 160 peanut butter cookies were sold and 80 chocolate chip cookies were sold.
Hope this helps!
