Trolls, tolls, and systems of equations | Algebra II | Khan Academy

TL;DR

In order to cross a bridge and save someone, a person must solve a riddle involving a troll and a system of equations.

Transcript

You are traveling in some type of a strange fantasy land. And you're trying to get to the castle up here to save the princess or the prince or whomever you're trying to save. But to get there, you have to cross this river. You can't swim across it. It's a very rough river. So you have to cross this bridge. And so as you approach the bridge, this tr... Read More

Key Insights

• 🧌 The riddle involves a toll troll, a bridge, and the need to save someone in a fantasy land.
• 🧌 The troll offers a riddle instead of accepting the toll payment.
• 💁 The problem can be solved through a system of equations using the given information.
• 🆘 Representing the clues mathematically helps in finding a solution.
• 🧌 The number of $5 and $10 bills the troll has can be determined by satisfying both equations.
• 🥺 Solving a system of equations leads to finding a solution.
• 🍧 Having only one equation is insufficient to solve the riddle.

Questions & Answers

Q: How can the person cross the bridge without paying the $5 toll?

The person can solve the troll's riddle by determining the number of $5 and $10 bills the troll has through a system of equations. By finding a solution that satisfies both equations, the person can cross the bridge without paying.

Q: Can the person solve the riddle if they only have one equation?

No, solving the riddle requires a system of equations. With only one equation, there are multiple combinations of $5 and $10 bills that could add up to 900 and $5,500.

Q: What is the significance of representing the clues mathematically?

By representing the clues mathematically, it becomes easier to manipulate and solve the equations. It allows for a systematic approach to finding the solution.

Q: Why is it important to set variables for the number of $5 and $10 bills?

Setting variables allows us to represent the unknown quantities in the riddle. It helps us express the relationships between the variables and the given information.

Summary & Key Takeaways

• A person needs to cross a bridge to reach a castle but must pay a $5 toll, which they cannot afford.

• The toll troll offers a riddle instead, stating that they have a total of 900 $5 and $10 bills, with a total value of $5,500.

• The person must figure out the number of $5 and $10 bills the troll has.

• The problem is solvable through a system of equations.