At first I thought the game was okay, it must be a teenager thing. But then I was hooked. I just need a few more coins so that I could upgrade my elixir storage, and if I upgraded my elixir storage then I could upgrade my gold storage, and if I upgrade my gold storage I could upgrade my elixir collector. You see what they did there? Yes, one variable depends on the other. Right now I'm saving up my gold so that I can upgrade my wizard tower to level 2 (a whopping 360,000 coins) and my elixir so that I can upgrade my barracks to level 7 (240,000 elixir).

Last night I asked myself if it was worth it. Should I upgrade my gold mine or let it go? When you upgrade a goldmine, you are unable to collect any gold during that time. Here are the details: My one goldmine is at level 7 and collects 1600 coins per hour. It costs 28,000 elixir to upgrade to level 8 and takes 24 hours to do this. Once I'm at level 8 the goldmine will collect 1900 coins per hour. I thought to myself "Do I really want to upgrade and not have any coins collected in this 24 hour period? Is it worth it?" And then it hit me.....this is ALGEBRA!!!

Let x represent the number of hours and let y represent the coins collected.

Equation without upgrading: y = 1600x + 38400 (the 38400 is the amount collected during the 24 hr period)

Equation without upgrading: y = 1900x + 0 (0 because you are unable to collect coins from that mine during the upgrade)

At what time with the coins be equal in amount?

Graphically:

Algebraically:

1600x + 38400 = 1900x

38400 = 300x

128 = x

5 1/3 days!!!

#### I need 360,000 coins to upgrade my wizard tower.

It would take 128 hours (or 5 1/3 days) for this upgrade to be worth it.

You can see from this screen shot that I have 201,785 coins right now.

Now my question is, "Will it be faster to collect these 360,000 coins by upgrading this goldmine or by leaving it alone?"

I have a total of 5 goldmines:

Goldmine 1 Level 8 1900 coins per hour

Goldmine 2 Level 8 1900 coins per hourGoldmine 3 Level 7 1600 coins per hour (thinking about upgrading this one)

Goldmine 4 Level 8 1900 coins per hour

Goldmine 5 Level 3 500 coins per hour

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I collect a total of 7800 coins per hour without the upgrade. I need 360,000 - 201,785 = 158,215 more coins to upgrade my wizard tower. That would take 158215 / 7800 = 20.3 hours.

Since this would take less than 24 hours to do, it wouldn't make sense to upgrade the gold mine.

I haven't tried any of this with my students yet, but I can't wait to see what individual questions they come up with for their own villages.