Question

I need to find the cost per table, the linear equation and the cost for making 15 tables

Answer 1

Explanation:

Let the cost of tables be C

Let the number of tables be"x"

If the cost of making 14 tables is $1,460 and the cost of making 17 tables is $1625, this can be expressed in the coordinate form of (C, x) to have two coordinates (14, 1460) and (17, 1625)

The general linear equation will be of the form C = mx + b

Get the rate of change "m"

$\begin{gathered} m=\frac{C_2-C_1}{x_2-x_1} \\ m=\frac{1625-1460}{17-14} \\ m=\frac{165}{3} \\ m=55 \end{gathered}$

Get the intercept "b" of the linear equation;

$\begin{gathered} 1460=55(14)+b \\ 1460=770+b \\ b=1460-770 \\ b=690 \end{gathered}$

Get the required linear equation:

$C(x)=55x+690$

Get the cost per table. When x = 1

$\begin{gathered} C(1)=55(1)+690 \\ C(1)=745 \end{gathered}$

Get the cost per for making 15 tables

$\begin{gathered} C(15)=55(15)+690 \\ C(15)=825+690 \\ C(15)=\ 1515 \end{gathered}$

Hence the cost of making 15 tables is $1515