How to solve this trigonometry question?

Question

You pay $145 for canning supplies plus $0.75 for each food item you can.

a. How many canned items must you complete for the average cost per canned item to fall to $1?

 

b. What happens to the average cost as you complete more canned items?

As the number of canned items increases, the average cost approaches $[  ?  ]

Answer 1

Er, this doesn't qualify as trig question. I can still answer it, though, as can you.

The average cost function is:

C-ave = Total cost   / number of items

In your case, that would be:

C-ave = (145 + 0.75X) / X   = 145/x  + 0.75

A)

If we plug in the $1 for C-ave, we get:

   1 = 145 / X + 0.75

-0.75              - 0.75

0.25 = 145 / X

You can rewrite this as:

1 = 145

 4     X

Cross-multiply and you get:

X = 580

B) as X increases, the supply cost falls lower while 0.75 stays the same, reducing the average cost more and more.

C) At extremely huge values, the 145 all but disappears into a tiny decimal, tiptoeing toward zero.

     That means you slowly approach 0.75 as an answer.