Question

Antoine bought a new electric guitar that cost \[\$588.60\] after 9 percent sales tax was added. What was the price of the guitar without tax?
(a) \[\$536\]
(b) \[\$540\]
(c) \[\$542\]
(d) \[\$545\]
(e) \[\$548\]

Answer 1

Hint: If the price of the guitar without tax was \[\$x\], then calculate 9 percent of x add it with x and the result will be 588.60. Form an equation and solve it of x.

Complete step-by-step answer:
Let us assume that the price of the guitar without tax was \[\$x\].
It is given in the question that 9 percent sales tax was added with the actual price.
Therefore, 9 percent of x will be:
$\Rightarrow x\times \dfrac{9}{100}=\dfrac{9x}{100}$
If we add the tax with our actual cost we will get the buying cost. Therefore,
$x+\dfrac{9x}{100}=588.60.....(1)$
Now we will solve the equation (1) to find out the value of x.
$\Rightarrow \dfrac{100x+9x}{100}=\dfrac{58860}{100}$
We can cancel out the 100 from both the denominators. Therefore,
$\Rightarrow 109x=58860$
By dividing both sides of the equation by 109, we will get:
$\Rightarrow x=\dfrac{58860}{109}$
$\Rightarrow x=540$
Therefore, the price of the guitar without tax was \[\$540\].
Hence, option (b) is correct.

Note: Remember that the tax is always applied on the actual price. So, do not find out the 9 percent of 588.60 and then subtract it from 588.60.