What is a variable? | Introduction to algebra | Algebra I | Khan Academy

Summary

The script explains the concept of a variable in algebra using a restaurant worker's hourly wage and tips as an example. It illustrates how the worker's total earnings can vary due to fluctuating tips, which are considered a variable. The script clarifies that variables can represent changing values and may be symbolized by letters or even unconventional symbols like 'star', emphasizing the flexibility in algebraic expressions.

Takeaways

• 💼 The speaker works in a restaurant and earns a fixed hourly wage of $10.
• 💰 In addition to the hourly wage, the speaker receives variable tips, which can fluctuate significantly from hour to hour.
• 🍽️ Tips can be high during busy hours, such as lunchtime, and low during slower periods, such as after a peak rush.
• 📈 The total earnings in an hour are calculated by adding the fixed hourly wage to the variable tips received.
• 🔢 The speaker uses the expression '10 plus tips' to represent the total hourly earnings, where 'tips' is a variable that changes.
• 💵 An example is given where during lunchtime, the speaker might earn $30 in tips, making the total hourly earnings $40.
• 📉 In contrast, during a slower hour, the speaker might only earn $5 in tips, resulting in a total of $15 for the hour.
• 🆎 The concept of a variable in algebra is introduced as a symbol that can take on different values, like the tips in this scenario.
• 📝 Instead of using the word 'tips', algebra often uses simpler symbols like 't' or 'x' to represent variables for ease of calculation.
• 🔄 The value of the variable 't' is substituted into the expression to calculate the total earnings for different scenarios.
• 📖 The script explains the concept of variables in algebra by using a relatable real-world example, making it easier to understand.

Q & A

What is the base hourly wage mentioned in the script for working in a restaurant?

The base hourly wage mentioned in the script is $10.

How is the amount of tips described in the script?

The amount of tips is described as variable and can change dramatically from hour to hour, depending on factors like the time of day or special events at nearby establishments.

What does the script use as an example of a high tip amount during lunchtime?

The script uses $30 as an example of a high tip amount during lunchtime.

How much total would the server make in an hour if they received $30 in tips?

If the server received $30 in tips, their total hourly earnings would be $40, which is the sum of their $10 hourly wage and the $30 in tips.

What scenario causes the server's tips to decrease dramatically?

The server's tips decrease dramatically when the restaurant slows down after the lunch hour, possibly due to a big sale at a nearby restaurant.

What is the total amount the server makes in an hour if their tips drop to $5?

If the server's tips drop to $5, their total hourly earnings would be $15, which includes their $10 hourly wage and the $5 in tips.

Why do we use variables in algebra instead of whole words?

We use variables in algebra instead of whole words because it is easier and more efficient to write and manipulate in mathematical expressions.

What symbol is suggested in the script to represent tips in an algebraic expression?

The script suggests using 't' as a symbol to represent tips in an algebraic expression.

What happens to the expression '10 + t' when t equals 30?

When t equals 30, the expression '10 + t' evaluates to $40.

What happens to the expression '10 + t' when t equals 5?

When t equals 5, the expression '10 + t' evaluates to $15.

What is the definition of a variable as explained in the script?

A variable, as explained in the script, is a symbol that represents varying values.