Question

Maizah bought a pair of pants and a briefcase at a departmental store. The sum of the prices of the pants and the briefcase before the sales tax was \[\ $ 130.00\] . There was no sales tax on the pants and a $ 9\% $ sales tax on the briefcase. The total Maizah paid, including the sales tax, was \[\ $ 136.75\] . What was the price in dollars, of the pants?

Answer 1

Hint: For solving this question we will first find the sales tax by subtracting the price of the pants and briefcase from before and after. And by assuming the price of the briefcase be $ x $ . Then we will calculate the $ 9\% $ of $ x $ which will equal the sales tax. And by solving for the value of $ x $ we will have the solution.

Complete step-by-step answer:
Here first of all we will see the values given to us, so it is given that the price of the pants and the briefcase before the sales tax was \[\ $ 130.00\] .
And the price of the pants and the briefcase after the sales tax was \[\ $ 136.75\] .
Therefore, the sales tax on the pant and the briefcase will be
 \[ \Rightarrow \ $ 136.75 - \ $ 130.00\]
And on solving the above subtraction, we get
 \[ \Rightarrow \ $ 6.75\]
Now let us assume that the $ x $ will be the price of the briefcase.
Therefore, according to the question, the equation framed will be given by
 $ \Rightarrow 9\% {\text{ of x = }}6.75 $
And removing the percentage and writing the above line mathematically, we get
 $ \Rightarrow \dfrac{9}{{100}}{\text{ }} \times {\text{ x = }}6.75 $
And on taking the constant term to one side, we get the equation as
 $ \Rightarrow x = \dfrac{{6.75 \times 100}}{9} $
And on solving the above equation, we get
 $ \Rightarrow x = 75 $
Therefore, the price of the briefcase will be \[\ $ 75\]
For the pants price,
The price of the pants price will be calculated as
 $ \Rightarrow \ 130 - 75 $
And on solving the subtraction, we get
 $ \Rightarrow 55 $
Hence, the price of the pants will be \[\$ 55\] .
So, the correct answer is “ \[\$ 55\] ”.

Note: For solving such a type of problem we just have to know how to frame the equations from the information given then only we can solve it. Also while solving this question if we want to remove the complexity of the solution then we can expand the decimal then the like term will cancel each other and will be easier to solve then.