Lure of the Labyrinth: Vending Machine | Level 2 Walkthrough

Welcome to Math with Mr. J. In this video, I'm going to walk through level two of the Lore of the Labyrinth vending machine game, which you can play to learn about systems of equations in algebra. Research shows that the best way to learn from the game is by playing it before learning algebra more formally. It's okay if you don't finish the game. The important part is to experiment, restart, and try different strategies. So before I explain the math, take 10 minutes to play level 2 of the vending machine game. This is a challenge level, so I recommend getting a sheet of paper to write down notes. While you play, think about these questions. What strategies are you trying? And how are your strategies changing over time. Pause this video and click the link below or in the description to play the game now. In the game, you are approached by a very hungry monster. The monster gives you coins to buy snacks from the vending machine, but you're not a monster. You don't know what the monster coins are. You'll have to figure out how much each coin is worth, then buy the tasty pack to feed the the hungry monster. There are many different ways to solve level 2. Did you come up with any creative strategies? Share them in the comments below. I'm going to walk through one possible strategy to solve level 2. Level 2 is a challenge level, so if you haven't finished the game yet, watch the first half of this walkthrough. Then try the game again using this as a hint. The monster gave us three different types of coins. Blue coins, which have round eye pupils. Green coins, which have slit cat eye pupils. And pink coins, which have speckled eye pupils. This level is a lot harder than level one. The vending machine won't let you spend three coins of the same kind. One strategy is to focus on two of the coins first. I'm going to try blue blue, green, then blue, green, green. Look at these two equations. Notice that the only difference between the left side of the two equations is that one blue coin has been swapped out for a green coin. These two blue coins stay the same, and these two green coins stay the same. On the right side of the equation, we can see that the total value of the coins increases from 8 to 13. so it increases by five. Since everything else between the equations is the same, this means that the green coin has to be worth five more than the blue coin. So green equals blue plus five. If you haven't finished the game yet, this is a great place to pause and try the game again using this strategy as a hint. Now that we know green is worth five more than blue, we can go back to the first equation and replace the green coin with blue plus five. That gives us three blue coins plus five. And that all adds up to eight. So let's ask ourselves, what number plus five gives us eight? Well, three. That means our three blue coins have to equal three. And if three coins equal three, each individual coin has to be worth one. And let's check that. One plus one plus one gives us three, plus that five equals eight. It works. The blue coin is worth one. Now that we know that the blue coin equals one, we can use that to figure out the green coin. We know that a blue coin plus 5 equals a green coin. The blue coin worth 1 plus 5 gives us 6. So the green coin is worth 6. Now that we know how much the blue and green coins are worth, we can use any combination to figure out how much the pink coin is worth. Try it yourself. Pause this video and solve for how much the pink coin is worth. What answer did you get? I got seven for pink. Now that we know how much each coin is worth, we can figure out which coins to use to buy the highlighted snack. We can plug in the coin values to find the combination that equals the cost of the snack. So for our example here, 19, let's try two of our biggest coins. The pink coin first, so seven plus seven, that gives us 14. We would need five more to get to 19. But the closest coin that we have is green, which is worth six. So if we use pink, pink, green, we would get seven plus seven plus six. That equals 20. So this is one more than the snacks price. The green coin is worth one less than the pink coin. So if we swap out one of the pink coins for a green coin, we get 7 plus 6 plus 6, which does equal 19. Now the monster swaps out one of your coins for a new orange coin, which has two missing corners. We can use the same process as before to find the value of the new coin. We have two green coins plus one orange coin and that equals 20. Since each green coin is six, together those two greens give us 12. So 12 plus that orange coin has to equal 20. How much more do we need to go from 12 to 20? Well, we need eight more. That tells us that the orange coin is worth eight. Finally, we can buy the tasty pack and feed the hungry monster. We know that the blue coin is worth one, the green coin is worth six, and the orange coin is worth eight. Which three coins should we spend to buy the tasty pack, which costs 10. Now we can use the same organized trial and error strategy that we used before. We can try a combination, then swap out a coin or coins to get a closer value. Pause the video and try this yourself. So which coins did you use? I used two blue coins and one orange coin. To check this answer, we can replace or plug in how much each coin is worth. So 1 plus 1 plus 8. This adds up to 10. So let's go ahead and spend these coins to buy the tasty pack. So there you have it. There's a walkthrough on one possible way you can solve level 2 of the vending machine game. Now, how does this game relate to math? This game builds algebraic reasoning skills through a real life, well, monster life, problem of solving for the values of unknown coins. Since we couldn't pay three of the same coin, we had to solve for two unknown coin values at the same time using two different equations. This is called a system of equations and is a core part of algebra and higher level math. The logic we used in the walkthrough today builds a strong foundation for math problem-solving strategies, such as substitution and elimination. By playing this level, you've started to learn solving two-step equations, evaluating expressions with two variables, how to solve systems of equations, and writing equations from word problems. I dropped links to more videos and examples down in the description. Those are great follow-ups to this game. For more details about the game, check out the intro and level 1 walkthrough videos here.