Question

Jenny’s moving bill was \(450 before taxes and tips. If taxes are 6% and she also wants to tip her three professional movers \)20 each, what does her total bill equal? (A) \(497 (B) 498.20 (C) \)537 (D) $540.60

Short answer

The total bill equals \( \boxed{\text{(C)} \: \$537} \).

Step-by-step solution

Calculate the tax amount

To find the tax amount, we will multiply the original cost by the tax rate (in decimal form). Tax amount = Original cost × Tax rate = \(450 × 0.06 = \)27

Calculate the tip amount

To find the tip amount, we will multiply the amount tipped per mover by the number of movers. Tip amount = Amount tipped per mover × Number of movers = \(20 × 3 = \)60

Calculate the total bill

Now, we simply add the original cost, tax amount, and tip amount to find the total bill. Total bill = Original cost + Tax amount + Tip amount = \(450 + \)27 + \(60 = \)537 The output of our calculation matches answer choice (C). Therefore, her total bill equals: \( \boxed{\text{(C)} \: \$537} \)

Key concepts

Percentage Calculation

Calculating percentages is a fundamental skill in math, required to understand various financial transactions, including taxes, discounts, and interest rates. A percentage represents a part out of 100. To convert a percentage to a decimal, which is necessary for calculations, you simply divide by 100. For instance, a 6% tax rate becomes 0.06 as a decimal (\( \frac{6}{100} = 0.06 \)).

When computing the amount of tax on Jenny's moving bill, we apply this basic principle of percentage calculation. The tax is calculated by multiplying the percentage (converted to a decimal) by the total amount before taxes. So for Jenny's moving bill of \(450, the 6% tax is determined as follows:

Tax amount = Original cost × Tax rate
= \)450 × 0.06
= \(27

This \)27 is the additional cost due to tax on top of the original bill.

Tax Computation

In practical terms, tax computation involves determining the additional amount paid on goods and services. This is applicable to a wide range of everyday situations from shopping to professional services, like moving services in Jenny's case. The key to handling taxes correctly is to know the tax rate which is usually given as a percentage.

To compute the tax for Jenny’s moving service, a tax rate of 6% is applied to the original cost. As mentioned, this percentage must be converted to a decimal format before the multiplication process starts. This process is representative of real-world scenarios where understanding how to calculate tax is essential for managing personal finances effectively.

Tipping Etiquette Math

Tipping is a common practice in many service-oriented industries, and it is typically expressed as a percentage of the total bill or as a fixed amount per service provider. An understanding of tipping etiquette math is important as it displays respect for those providing a service, showing appreciation through a monetary supplement.

In Jenny’s scenario, instead of a tipping percentage, she opts to give a fixed sum of \(20 per mover. She hires three movers, which means the tipping calculations are straightforward multiplications. Here it is important to note that this fixed-sum approach simplifies the arithmetic involved:

Tip amount = Amount tipped per mover × Number of movers
= \)20 × 3
= \(60

The total tipping amount is therefore \)60. Keeping in mind the difference between fixed-sum tips and percentage-based tips will help you navigate through various real-life tipping situations.

Basic Arithmetic

The heart of many math problems, including ones involving financial transactions, lies in basic arithmetic operations: addition, subtraction, multiplication, and division. In our exercise featuring Jenny's moving bill, we put into practice addition by compiling the original cost, taxes, and tips to find the total expenditure.

After calculating the individual amounts for taxes and tips, using multiplication as shown in the prior sections, we add these to the original amount to find the total:

Total bill = Original cost + Tax amount + Tip amount
= \(450 + \)27 (the tax) + \(60 (the tips)
= \)537

Understanding basic arithmetic operations and their practical applications is crucial for foundational math literacy and for managing everyday financial tasks.