Question 635823
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 ${{{x}}} .
The tax would be ${{{0.05*x}}}
For a customer that must pay sales tax, the bill (in $) would be
{{{x+0.05x=(1+0.05)x=1.05x}}}
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.
{{{1.05x=145.90}}}
We must solve that equation for {{{x}}} .
Dividing both sides of the equal sign by {{{1.05}}} we get
{{{1.05x=145.90}}} --> {{{1.05x/1.05=145.90/1.05}}} --> {{{highlight(x=138.95)}}} (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.