Question

Economics Mr. Diaz took his mother out for dinner. The total for the items they ordered was \(\$ 20\) a. Mentally calculate the \(5 \%\) sales tax on the order. b. Mr. Diaz wants to leave a \(20 \%\) tip on the food cost plus the sales tax. Mentally calculate how much the tip should be.

Short answer

The sales tax is \$1\, and the tip should be \$4.2\.

Step-by-step solution

- Calculate the Sales Tax

To find the sales tax, multiply the cost of the items by the sales tax rate. Here, the cost is \$ 20\ and the sales tax rate is \ 5\%. So, \[ \text{Sales Tax} = 20 \times \frac{5}{100} = 20 \times 0.05 = \$ 1 \]

- Calculate the Total Cost Including Sales Tax

Add the sales tax to the original food cost to find the total cost. So, \[ \text{Total Cost} = 20 + 1 = \$ 21 \]

- Calculate the Tip

To find the tip, multiply the total cost including sales tax by the tip rate. Here, the total cost is \$ 21\ and the tip rate is \ 20\t%. So, \[ \text{Tip} = 21 \times \frac{20}{100} = 21 \times 0.20 = \$ 4.2 \]

Key concepts

mental arithmetic

Mental arithmetic is a valuable skill that allows you to calculate numbers in your head without using a calculator or paper. It's not only quick but also improves your number sense and problem-solving abilities. For example, in our exercise, calculating the sales tax mentally involves simple multiplication. To find the 5% sales tax on \(20, multiply 20 by 5%, which is the same as multiplying by 0.05. This can be expressed as:

\( 20 \times 0.05 = 1 \)

This means the sales tax is \)1. Additionally, mental arithmetic comes in handy when calculating tips. To find a 20% tip on a \(21 total, you multiply \)21 by 20%, or 0.20:

Looking at it:\( 21 \times 0.20 = 4.2 \)

Practice mental arithmetic regularly to speed up your calculations and build confidence in your math skills.

percentage calculations

Understanding percentage calculations helps you quickly determine parts of a whole. Percentages are a way of expressing numbers as parts of 100. For instance, a 5% sales tax means 5 parts out of 100, or 5/100. You can convert this fraction into a decimal for easy multiplication:
\( \frac{5}{100} = 0.05 \)
Multiplicy the price of the meal (\(20) by this decimal to find the tax:
\( 20 \times 0.05 = 1 \)
the sales tax is \)1. Likewise, to calculate the tip, convert the 20% to a decimal:
\( \frac{20}{100} = 0.20 \)Next, multiply by the total cost including tax (\(21):
\( 21 \times 0.20 = 4.2 \)
the tip amount is \)4.20. By mastering percentage calculations, you can tackle problems involving discounts, interest rates, and more.

basic algebra

Basic algebra is not just for solving equations—it's for understanding relationships between numbers and operations in real-life scenarios. In the given exercise, you use basic algebra to understand and solve the problem of adding sales tax and calculating the tip.
First, you determine the sales tax: \( 20 \times 0.05 = 1 \)This gives you the sales tax of \(1. Adding this to the \)20 cost of the meal, you get the total cost. Summing these up: \( 20 + 1 = 21 \)So, the total cost is \(21. Next, you use this new total to calculate the tip: \( 21 \times 0.20 = 4.2 \)which means the tip is \)4.20.Basic algebra helps to simplify and solve problems involving multiple steps like this. Practice by breaking down larger problems into simpler steps and solving them one at a time. Algebra can make complex problems easier by showing the relationships between different parts of the problem.