Problem 62 If an item costs $\$ 36.95$, t... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 1: Problem 62

If an item costs $\$ 36.95$, then what is the total after adding $9 \% \%$ tax?

Short Answer

Expert verified

The total cost after tax is $40.28.

Step by step solution

Understand the Problem

To find the total cost after adding tax, we need to calculate 9% of the item's price and then add the resulting tax amount to the original price.

Calculate the Tax Amount

Find 9% of the original price of the item, which is $36.95. This can be calculated as follows: \[\text{Tax Amount} = 0.09 \times 36.95\]Calculate this to get the tax amount.

Perform the Multiplication

Calculate $0.09 \times 36.95$.\[0.09 \times 36.95 = 3.3255\]Round this to two decimal places, which is the standard in currency calculations, to get $3.33.

Add the Tax to Original Price

Now, add the tax amount back to the original price:\[36.95 + 3.33 = 40.28\]This gives us the total price after tax.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percentage Calculation

Understanding percentage calculations is key when determining added costs like taxes. A percentage represents a part of a whole divided into 100 equal portions. In our case, the 9% tax means we consider 9 out of every 100 parts of the item's price. Calculating percentages involves converting the percentage into a decimal format. Here, turning 9% into decimal form involves dividing by 100, resulting in 0.09.
This decimal is then multiplied by the original price to determine the amount added by the tax. For instance, with a price of $36.95, the tax is calculated as follows:

Convert the percentage: 9% becomes 0.09.
Multiply this decimal with the item cost: 0.09 x 36.95

This gives the tax amount to be added to the original price.

Currency Rounding

Currency rounding is a common practice used to simplify monetary amounts. It's particularly important when dealing with prices and taxes, where amounts are typically rounded to two decimal places to represent cents. This is because our currency system is based on dollars and cents. In our example, the calculated tax amount was $3.3255.
For currency purposes, we need to round this to the nearest cent. Rounding follows specific rules:

If the third decimal is 5 or more, the second decimal is increased by one (3.3255 becomes $3.33).
If the third decimal is less than 5, the second decimal remains the same (such as, $3.324 becomes $3.32).

Applying these rules ensures that the total cost is accurate and easy to manage when money changes hands.

Basic Arithmetic Operations

Basic arithmetic forms the everyday foundation of calculations. These operations include addition, subtraction, multiplication, and division. They are crucial in situations like calculating total costs after adding sales tax. In our exercise, these basic operations guide the solution:
The first step involved multiplication, where the tax percentage, converted to decimal form, multiplied the item's price to find the tax amount. Then, addition came into play to find the final price. The original price ($36.95) was added to the rounded tax amount ($3.33):

Perform multiplication: 0.09 times 36.95 for the tax.
Then add this tax to the original price: 36.95 + 3.33 = 40.28.

This step finalizes the total cost, including tax.

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91影视

If an item costs \(\$ 36.95\), then what is the total after adding \(9 \% \%\) tax?

Short Answer

Step by step solution

Understand the Problem

Calculate the Tax Amount

Perform the Multiplication

Add the Tax to Original Price

Key Concepts

Percentage Calculation

Currency Rounding

Basic Arithmetic Operations

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