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Credit card processor charges, for each transaction, $2.9\% + \$0.30$.

I need to find an amount that covers that cost, from $\$5$ to $\$5,000$, on a per item basis, all while maintaining a small profit.

For example, a customer may want to purchase 3 items. Each item has a different price and possibly a different fee structure based on whether or not it's a for-profit purchase or non-profit purchase.

Item 1 is $\$10$ and for-profit so we need to account for the processing fee plus a $5\%$ profit.

Item 2 is $\$80$ and for-profit so we need to account for the processing fee plus a $5\%$ profit.

Item 3 is $\$25$ and non-profit so we need to account for the processing fee only- no profit.

What I cannot determine is a full-proof way to account for the fees all the way up to $5,000 without losing money on the processing fees.

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  • $\begingroup$ You have used the dollar sign. It has confused the mathjax interpreter. Please use something else like £. $\endgroup$ – Ali Caglayan Aug 19 '13 at 14:34
  • $\begingroup$ @jasonsfa98: Welcome to MSE! There is still a problem with the dollar signs. Also, do you have thought on the problem and can share what you have tried as it helps responders? Regards $\endgroup$ – Amzoti Aug 19 '13 at 14:49
  • $\begingroup$ I've set things inside MathJax with backslashes in front of the dollar signs and percent signs that are supposed to actually appear. The same thing works in standard LaTeX. $\endgroup$ – Michael Hardy Aug 19 '13 at 17:43
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I will ignore dollar signs. Suppose that $C$ is the cost of the product and we wish to charge $C + X$ for the product. The processing fee is $.029(C + X) + .3$. We need to solve $$(C + X) - (.029(C + X) + .3) \geq C$$ for $X$. In this equation $C + X$ is what we charge and $.029(C + X) + .3$ is the processing fee. If the difference is greater than $C$ we make a profit. There are probably other costs that are not mentioned in this problem. Presumably they are included in the value of $C$. In any event we need $$.971 X \geq .029 C + .3.$$ We can solve for $X$ as follows: $$X \geq \frac{.029 C + .3}{.971}.$$ There is no upper bound for the value of $X$.

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