Hello, daemon!
Including a 6.1% sales tax, a television set sold for $1591.50.
Find the price before the tax was added.
You might try some baby-talk on problems like these . . .
Let \(\displaystyle x\) = the retail price of the TV.
Sales tax is 6.1% of \(\displaystyle x\) . . . that is, \(\displaystyle 0.061x\)
So the total price is : \(\displaystyle \text{(Retail price) + (Sales Tax) } = \:x\,+\,0.061x\:=\:1.061x\)
We're told that this total was $1591.50: \(\displaystyle \,1.061x\:=\:1591.50\)
. . Divide both sides by 1.061: \(\displaystyle \;x\:=\:1500\)
Therefore, the retail price of the TV is $1,500.
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Check
\(\displaystyle 6.1\%\text{ of }1500\:=\:0.061\,\times\,1500\:=\:\$91.50\) sales tax
Hence, the full price is: \(\displaystyle \$1500\,+\,91.50\:=\:\$1591.50\)
. . . check!