Question

If the sales tax rate is $8.375\% $ in New York City, then how much would you pay for a pair of shoes in Manhattan that cost $\$ 125.00$? (Round your answer to the nearest cent.)

Answer 1

Hint: In order to determine the Selling price of a pair of shoes in New York City ,first calculate the overall tax by multiplying the percent value with the cost price. Convert the percent value into fraction by dividing it with 100 and then removing percent sign. Now Add the obtained tax value with the cost of shoes and round off the answer up to 2 decimal points to get the required answer.

Complete step by step solution:
We are given a word problem and form this we have to form some mathematical expression to get the answer.
According to the question , we are given the sales tax rate in New York City as $8.375\% $ and the cost of a pair of shoes in Manhattan as $\$ 125.00$.
In this question , we are supposed to find out the total cost of a pair of shoes in New York City.
Now, If we try form a mathematical equation from the statement in the question , we have the price of shoes in New York as
Selling Price(New York)=Price of Shoes(Manhattan) + Tax----------(1)
Since we are given that the tax is $8.375\% $ of the cost, then we have the overall tax as
$tax = 8.375\% \, \times \,125$
As we know, to convert percent into its equivalent fraction , we have to divide the percent value with 100 and remove the percent sign. We can rewrite the above equation as
$tax = \dfrac{{8.375}}{{100}}\, \times \,125$
Now putting this expression of tax in the actual equation of selling price i.e. equation (1), we get
Selling Price( New York)$ = 125 + \dfrac{{8.375}}{{100}}\, \times \,125$
Pulling out common $125$from both the terms and simplifying further ,we get
Selling Price( New York)=
$
   = 125\left( {\dfrac{{8.375}}{{100}}\, + \,1} \right) \\
 \Rightarrow 125\left( {\dfrac{{8.375 + 100}}{{100}}} \right) \\
  \Rightarrow 125\left( {\dfrac{{108.375}}{{100}}} \right) \\
  \Rightarrow \dfrac{{13546.875}}{{100}} \\
 \Rightarrow 135.46875 \\
 $
$ = 135.47$(Rounded off to nearest cent)
Therefore, the selling price for a pair of shoes in New York City is equal to $ = 135.47$(nearest cent)

Additional Information:
Mathematical equation : A Mathematical equation can be defined as the mathematical statement which contains an equal symbol $ = $ in between two algebraic expressions that share the same value .
A algebraic expression can contain any number of variables generally we take 2-3 variables
Let assume a expression
$5x + 9 = 24$
It is a mathematical equation having LHS (Left-Hand-Side) equal to RHS (Right-Hand-Side)
Where $x$ is the variable
5 is the coefficient of variable $x$
And $24,9$ are the constants

Note: 1. Read the statement carefully in order to convert them into mathematical expressions.
2.The answer obtained in the end is actually the rounded off value. The answer by actual calculation is equal to $135.46875$
3. Questions from which we have to obtain the mathematical expression are known as word problems.
4. Remember , in word problem ‘of’ in between two values is always considered as the $ \times $sign .For example: $\dfrac{1}{2}$of 42 is equivalent to $ = \dfrac{1}{2} \times 42 = 21$