Question

A company has a manufacturing plant that is producing quality clocks. They find that in order to produce 240 clocks in a month, it will cost $7760. Also, to produce 450 clocks in a month, it will cost $11750. Find an equation in the form y=mx+b, where x is the number of clocks produced in a month and y is the monthly cost to do so.Answer: y=

Answer 1

Given the equation:

$y=mx+b,$

if you substitute the given data, you get the following system of equations:

$\begin{gathered} 7760=240m+b, \\ 11750=450m+b. \end{gathered}$

Subtracting the first equation from the second one, you get:

$11750-7760=450m-240m+b-b.$

Simplifying you get:

$3990=210m.$

Solving for m, you get:

$m=\frac{3990}{210}=19.$

Substituting m=3990 in the first equation, and solving for b you get:

$\begin{gathered} 7760=19(240)+b, \\ b=7760-19(240), \\ b=3200. \end{gathered}$

Answer:

$y=19x+3200.$