i am lost on this problem !

Question

A manufacturing company finds that they can sell  items at  per item and  items at  per item. If the relationship between the number of items sold  and the price per item  is a linear one:

Find a formula that gives  in terms of :    

Now use the formula to find the number of items they will sell if the price per item is . They will sell _____ items if the price is .

Answer 1

Hi Rebecca,

This is a great question. Questions like this can be a bit difficult because they often change up the names of the variables we are used to working with. The key to working out a problem like this is to notice that q=x and p=y. However, let's still work this problem out in terms of q and p.

we have two sets of data.

(q₁,p₁)=(125,3.50)

and

(q₂, p₂₎=(350,2.00)

At this point you may realize that both data sets look a whole lot like coordinates. This is a good!!!

Because if they are coordinates than we can use the equation y=mx+b or in this case p=mq+b

Next, we need to remember the definition of slope:

m=rise/run ----> (p₂-p₁)/(q₂-q₁)

So, for this problem our slope would be:

m=(2.00-3.50)/(350-125)= -1.5/225 ----> -1/150

Now all we are missing in our equation is b.:

p=(-1/150)q+b

To find b we chose one of our two coordinates and subtract the q of the coordinate from the q of our equation and the p of our coordinate from the p of our equation.

p-3.50=(-1/150)(q-125)

distribute -1/150 to the x and 125

p-3.50=-1/150(q)+(5/6)

add 3.50 to both sides

p= -1/150(q)+13/3

Now, all you need to do is rearrange the equation in terms of q=? which I will let you try first. Let me know if you get stuck on this step and I will walk you through it.

You should check to make sure your equation is correct by plugging one of your coordinate's p's in for p and solving. It should equal the q of that same coordinate.

To solve the final question plug 1.50 in for p and solve for q

Please let me know if you have any questions or need help with anymore problems,

-Amanda G.