Use the proof type strong mathematical induction to prove that every positive integer greater than one is divisible by at least one prime number. That is, prove that the following formal statement is true, Vn e Z+, n > 1, Ep e Z+, p prime | (p | n) Half the points for this problem will be granted only if you show the correct form of the proof type. That is, showing formal start and end statements, explicitly proving any needed basis case, explicitly proving the strong mathematical induction step, and explicitly asserting that the requirements for strong mathematical induction have been met before you conclude the proof. You can use the Canvas math editor or English language sentences. You must use the 2-column statement/justification format for your proof. Every statement must be justified.

28 5 dollar bills

12 10 dollar bills

Step-by-step explanation:

You can write two equations to model this situation'

x will be the number of 5 dollar bills

y will be the number of 10 dollar bills

x+y=40

5x+10y=260

There are a couple of ways you can solve this but but I will be doing it through substitution because that looks easier (I can explain other methods if you're interested)

So we have x+y=40

If I subtract y from both sides and divide by -1 we get

-x+40=y

We can then plug this value in for y in the second equation

5x+10(-x+40)=260

Distribute the 10 and combine like terms to get

-5x+400=260

subtract 400 from both sides and divide by -5 to get

x=28

This means that there are 28 5 dollar bills. We can plug this value back in for x into our first equation to solve for y

28+y=40

Subtract 28 from both sides

y=12

This means that there were a total of 28 5 dollar bills and 12 10s

I doubled checked this in desmos and it checks out