SOLUTION: Please help me solve this equation. Thank you. Deducting Sales Tax... A tax -exmpt charity recieved a bill of $145.90 for a sump pump. The bill incorrectly included sales tax of

Question 635823: Please help me solve this equation. Thank you.
Deducting Sales Tax... A tax -exmpt charity recieved a bill of $145.90 for a sump pump. The bill incorrectly included sales tax of 5%. How much does the charity owe?

I know the correct way to think of the problem is... The origional price, a variable, + 5% of the origional price equals $ 145.90. I've came up with this so far...

5% is converted to 0.05
0.05 * 145.90 = 7.295
145.90 - 0.05 = 145.85
so would the answer be $ 145.85 ????

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
No, that's not right. Here is why.
The calculation
0.05 * 145.90 = 7.295
gives you 5% of 145.90.
That is 5% of the total bill, which included tax.
However, the sales tax was 5% of the unknown amount that you have to find (the price of the sump pump).
Let the price of the sump pump be $ .
The tax would be $
For a customer that must pay sales tax, the bill (in $) would be

That is 105% of the price, 100% of the price for the merchant, and $5% of the price (the sales tax) for the government.
That is how the merchant calculated (incorrectly) the bill for the tax-exempt charity.

We must solve that equation for .
Dividing both sides of the equal sign by we get
--> --> (rounding)
The price of the pump was $138.95, and that is all that the charity should pay.
The 5% tax on $138.95 calculates as
0.05*($138.95)=$6.9475, which rounds to $6.95.
The merchant added $138.95+$6.95=$145.90 to come up with the incorrect bill.
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