Linear models example 2 | Algebra I | Khan Academy

TL;DR

The video explains how to determine the volume of marbles and water in a tank based on certain parameters.

Transcript

• [Voiceover] William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it's completely full. If he uses 85 marbles, he will have to add 20.9 liters of water. What is the volume of each marble? All right, so let's think about it. The volume of the marbles p... Read More

Key Insights

• 🔇 The volume of the marbles plus the volume of the water should equal the volume of the tank.
• 🔇 The volume of each marble is calculated by dividing the total volume of the marbles by the number of marbles used.
• 💦 The amount of water needed can be determined using a linear function based on the number of marbles.
• 💦 For 200 marbles, 14 liters of water are needed.
• ✖️ The calculations involve solving equations and using basic multiplication and subtraction.
• 🔇 The volume of each marble is 0.06 liters, regardless of the number of marbles used.
• 🌍 The concept demonstrated in the video is an example of applying mathematical principles to solve real-world problems.

Questions & Answers

Q: What equation can be used to determine the volume of marbles and water in a tank?

The equation is V (Volume of marbles + Volume of water) = Volume of tank. It can be further simplified as 85M + 20.9 = 26, where M represents the volume of one marble.

Q: What is the volume of each marble?

By solving the equation, the volume of each marble is 0.06 liters. This is obtained by dividing 5.1 liters by 85.

Q: How can the amount of water needed be calculated for a specific number of marbles?

The amount of water needed (W) can be calculated using the linear function W = 26 - (0.06 * number of marbles). Substituting 200 for the number of marbles, 14 liters of water are required.

Q: What is the relationship between the number of marbles and the volume of water needed?

The volume of marbles (0.06 liters) is multiplied by the number of marbles to calculate the volume of marbles. This volume is then subtracted from the volume of the tank (26 liters) to determine the volume of water needed.

Summary & Key Takeaways

• The volume of the marbles plus the volume of the water should be equal to the volume of the tank.

• A linear function can be used to calculate the amount of water needed based on the number of marbles.

• By solving the equation, each marble has a volume of 0.06 liters, and 14 liters of water are needed if 200 marbles are used.