Math CentralQuandaries & Queries


Question from Michelle, a student:

Good day,

I would like to know if there is a particular equation to validate the following information:

I had to find the original cost of an item sold for 759.36$ before a 25% discount and 13% taxes.
I know we must use separate equations to obtain the answer but I am unsure how to write the equation to validate my answer.

please advise,



Hi Michelle,

If I understand this correctly you paid $759.36\$$ and this included a 13% tax and a discount of 25%. If this is correct then you went to the cashier with the discounted price, the cash register added the 13% tax and the cashier said you owed $759.36\$.$ Suppose the discounted price was $D\$$ then the cash register calculated

\[D\$ + 0.13 \times D\$ = 1.13 \times D\$ = 759.36\$\]

and hence

\[D\$ = \frac{759.36\$}{1.13}.\]

How much is this?

Suppose the original price was $P\$$ then the discount is 25% so the discounted price $D\$$ was 75% of $P\$.$ Solve for $P\$.$


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