# Math Lesson 8.1.3 - Expressing Events in a Shorter Way using Formulas

Welcome to our Math lesson on Expressing Events in a Shorter Way using Formulas, this is the third lesson of our suite of math lessons covering the topic of Writing Formulas and Substituting in a Formula, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

## Expressing Events in a Shorter Way using Formulas

We don't just use formulas to express scientific phenomena, they are also used to describe daily activities in a shorter way, especially when these activities are recurring and have the same routine. You may have used spreadsheets (like Microsoft Excel) to express a number of events involving the same variables in different situations. Thus, after writing the formula, you simply insert the input values and as a result, the output values appear automatically in the in the designated cells as shown in the figure below, where the average of all input values is calculated through the corresponding formula. Thus, instead of adding all values manually and dividing them by the number of values to calculate the average, we simply insert the input values in different cells (here from B3 to B12) and by means of the formula of average shown in the top-right part of the figure, we calculate the average of the given numbers (here 59, shown in the cell B14) with just a click.

Indeed, if we add all numbers manually, the sum is 590. Since there are 10 numbers in total, the average is 59 (590 ÷ 10). However, the formula method is more suitable as we simply replace all input values with others to obtain the average without having to add them manually.

Likewise, many companies use formulas to calculate the cost of services they provide to customers. This saves a lot of precious time for employees who deal with customers. For example, if the cost of a drink in a restaurant table is D = \$2.5 and the place reservation per person costs R = \$6, the bill B is calculated by the formula

B = N∙ (R + n ∙ D)

or more specifically,

B = N ∙ (6 + n ∙ 2.5)

where n is the number of drinks a person orders. In this scenario, we have assumed that all customers have ordered the same number of drinks. In this way, the waiter has to insert only the number of customers N in the restaurant table and the number of drinks per person n to calculate the bill.

### Example 3

Matt has £4,700 savings in the bank. He gets a job and is paid £12 for every hour he works. Assuming he spends nothing, write a formula for the amount of money (£M) Matt will have after he has worked for h hours.

### Solution 3

The amount of money Matt will have after working for h hours in the new job will add to his savings to give the total amount he will have. Thus, we can write

Total amount = Initial amount + Hourly salary × Hours worked

When written in symbols, this relation becomes

(£M) = £4,700 + £12 × h

On the other hand, when written as a formula, the above relation becomes

M = 4,700 + 12h

where M is the total amount of money Matt will have after h hours.

## More Writing Formulas and Substituting in a Formula Lessons and Learning Resources

Formulas Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
8.1Writing Formulas and Substituting in a Formula
Lesson IDMath Lesson TitleLessonVideo
Lesson
8.1.1Mathematical vs Word Sentences
8.1.2What is a Formula? How do we Write Formulas?
8.1.3Expressing Events in a Shorter Way using Formulas
8.1.4Substituting into a Formula
8.1.5Substituting in Formulas derived from Wordy Problems
8.1.6Finding the Inverse Formula

## Whats next?

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