Question

I need to find the cost per table, the linear equation and the total cost of making 24 tables.

Answer 1

We are told that the cost of making 14 tables is 1210 and that the cost of making 26 tables is 1750. If this is a linear relationship, this means that we want to find a line of the form

`y=mx+b`

where m is the slope and b is the y-intercept that passes through the given points.

In our case we are given the points (14,1210) and (26,1750). We will calcualte the slope m as follows: given poitns (a,b) and (c,d) the slope is given by the formula

`m=\frac{d\text{ -b}}{a\text{ -c}}=\frac{b\text{ -d}}{c\text{ -a}}`

In our case we have a=14, b=1210, c=26 and d=1750. So

`m=\frac{1750\text{ -1210}}{26\text{ -14}}=(540)/(12)\text{ }=45`

Note that this slope reprents the cost per table. So the cost per table is 45.

Now we want to find the value of b. So far the equation looks like this

`y=45x+b`

from this formula, we want that when x=14, then y=1210. So we get the equation

`1210=45\cdot14+b=630+b`

So if we subtract 630 on both sides, we get that

`b=1210\text{ -630=580}`

So the linear equation is

`y=45x+580`

this means that the cost of 24 tables is obtained by replacing the value of x by 24. So we get

`y=45\cdot24+580=1660`

So the cost for 24 tables is 1660