Problem

The cost of printing a math workbook is a setup cost plus a cost for each book printed. If 1000 books printed cost $\$ 14300$, and 5000 books printed cost $\$ 64300$, what is the setup cost for printing the math workbooks?

Solution

Step 1 :Let the setup cost be $x$ and the cost per book be $y$. We can set up two equations based on the given information:

Step 2 :\(1000x + 1000y = 14300\)

Step 3 :\(1000x + 5000y = 64300\)

Step 4 :Subtract the first equation from the second equation to eliminate $x$:

Step 5 :\(4000y = 50000\)

Step 6 :Divide both sides by 4000 to find the value of $y$:

Step 7 :\(y = 12.5\)

Step 8 :Now, substitute the value of $y$ back into the first equation to find the value of $x$:

Step 9 :\(1000x + 1000(12.5) = 14300\)

Step 10 :\(1000x + 12500 = 14300\)

Step 11 :Subtract 12500 from both sides to find the value of $x$:

Step 12 :\(1000x = 1800\)

Step 13 :Divide both sides by 1000 to find the value of $x$:

Step 14 :\(x = 1.8\)

Step 15 :So, the setup cost for printing the math workbooks is \(\boxed{1.8}\) dollars.

From Solvely APP
Source: https://solvelyapp.com/problems/31012/

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