how do i Calculate the number of zombies and soldiers at the start of each day from Day 1 to Day 5.

Question

A soldier can hunt down and kill 15 zombies a day. In the evening, each soldier can also recruit one new soldier from the people in the city who will join the army the following day and fight the zombies. However, each night, the zombies will fight back and each one will infect five normal people who then become zombies. You know that there are currently 60,000 zombies in the city.

Answer 1

Hi Jay from New York, NY...hope you're having a great weekend.

Great...a ZOMBIE question...your teacher is great to include this.

Well...I won't answer it for you...that's your job however...I will help you set it up...so you can understand how to do these kind of problems, making you a ZOMBIE pro.

Okay let's identify some things...things we know and things we don't know

       a soldier kills 15 zombies a day so we'll label that      15s

             so in 3 days, the so soldier kills:     15(3) = 45 zombies  Right?!

       there are 60,000 zombies in the city

       a soldier can recruit a NEW soldier each night, we label that    + n

       so with our original soldier and the new soldier each day we can write

             15s + n15  which reads the original soldier kills his 15 zombies

                              and each new soldier kills their 15 zombies.

       15(3) + (3)15  So in 3 days, the original soldier kills 15 zombies and 

                              3 new soldiers kill their 15 zombies for a total of

      45 + 45 = 90    90 zombies killed at the end of 3 days.

     15(s + n) = k     we can rewrite the equation. we know that each 

                              soldier kills 15 zombies each day and that each day a

                             new soldier is added to the original soldier's zombie

                              kill army, for the total of zombies killed, labeled   'k'

That is just one part of the equation. The other part of the equations needs to include the other information provided in your problem. You know each ZOMBIE infects 5 normal people each night...YIKES!!...with that noted....each night our equation has to include the number of new zombies. So another equation is for each night 5 times 60,000 or 300,000 new zombies...DOUBLE YIKES!!

However, at the same time, some of the zombies are being killed and some of the normal people are being make soldiers. How do we include this into our equation...

Now...I've give you some hints...I'm going to give you just a bit more, but I want you to finish this...you will need to know how to set up these kinds of problems. HINT: at the same time the soldiers are killing zombies, other zombies are creating new zombies. Which means we will need to subtract those zombies being killed from the original 60,000 zombies, BUT we need to include the NEW zombies being created each night.

Try putting you brain [before it gets eaten by a zombie]into the expressions you have already created/known. See if you can create an equation. If you need any further help...contact me on Wyzant.