Let x represent the number of envelopes stuffed

Question

Students stuff envelopes for extra money. Their initial cost to obtain the information for the job was $80.

Each envelope costs ​$0.06 and they get paid $0.07

per envelope stuffed. Let x represent the number of envelopes stuffed.

​(a) Express the cost C as a function of x.

​(b) Express the revenue R as a function of x.

​(c) Determine analytically the value of x for which revenue equals cost.



Answer 1

Hi Di,

Here are the worked solutions for your questions.

Part (a)

The total cost of this job is the initial cost plus the cost of the envelopes.

We are told the initial cost is 80 dollars.

The cost of the envelopes is equal to the cost per envelope times the number of envelopes. The cost per envelope is $0.06, and we were told that x is the number of envelopes.

So: cost of envelopes = $0.06/envelope * x envelopes = $0.06x

Therefore, the total cost (C) is C = 80 + 0.06x dollars.

Part (b)

Revenue is the total money earned by the students for this job. Since stuffing envelopes is the only thing they earn money for on this job, total revenue is the amount of money they earn for stuffing envelopes.

Money from envelopes= $0.07/envelope * x envelopes = $0.07x.

Therefore, the total revenue (R) is R = 0.07x dollars

Part (c)

This part is asking us to figure out how many envelopes must be stuffed for the students to break even. We can calculate this by setting the Cost equation from Part (a) and the Revenue equation from Part (b) equal to one another and then solving for x.

1. Cost = Revenue: 80 + 0.06x = 0.07x
2. Subtract 0.06x from both sides to get all x-terms one side, combine like terms:
3. 80 + 0.06x -0.06x = 0.07x -0.06x
4. 80 = 0.01x
5. Divide both sides by 0.01 to solve for x:
6. 80/0.01 = 0.01x/0.01
7. 8000 = x

Therefore, the students must stuff 8000 envelopes to break even.

Hope this helps!