Question

can i know your answer,please?The cost of printing x copies of a pamphlet is $C, where C = Ax + B for certain constants
A and B. If it costs $5,000 to print 10,000 copies and $6,000 to print 15,000 copies, how much
it will cost to print 100,000 copies?

Answer 1

Answer on question #39490, Math, Algebra

The cost of printing x copies of a pamphlet is $C, where C = Ax + B for certain constants A and B. If it costs $5,000 to print 10,000 copies and $6,000 to print 15,000 copies, how much it will cost to print 100,000 copies?

After this task we can build next system of equations:

$$\begin{array}{l} \left\{A * 10000 + B = 5000 \quad (1) \right. \\ \left\{A * 15000 + B = 6000 \quad (2) \right. \\ \end{array}$$

We will subtract (1) from (2) (2)-(1) and we will get:

$$A * 5000 = 1000 \quad \Rightarrow \quad A = \frac{1}{5}$$

So,

$$\frac{1}{5} * 10000 + B = 5000 \quad \Rightarrow \quad B = 3000$$

Now we know A and B, and can calculate how much it cost to print 100000 copies:

$$A * 100000 + B = \frac{1}{5} * 100000 + 3000 = 23000$$

**Solution:** It will cost $23000.