Inequality Word Problem

Question

Mr. Williams has $100 to spend on tickets for a show. Child tickets cost $8 less than adult tickets. He buys 8 adult tickets. What is the maximum number of child tickets he can purchase after purchasing the adult tickets?

Answer 1

Mr. Williams has that $100 for tickets because Mrs. Williams is the victim of "gender" inequality and performing arts microaggression and macroaggression perpetrated upon her by Mr. Williams ever since he learned she was not born with the name Caitlyn, but Bruce!

 

Woman of the Year his asterisk!

Answer 2

Let $ x = price of adult ticket

 

Now, price of a child ticket = $ (x-8) 

 

The man buys 8 adult tickets. So, he pays 8x dollars for this.

 

Let us say he buys 'n' child tickets 

 

8x + n(x-8) <or= 100 is the inequality.

 

Or, n <or= 100-8x/(x-8)

 

     n is a positive number, therefore, x >or= 9    

 

For x=9, n = 100-72/1 = 28

 

For x=10, n = 100-80/2 =10  

 

For x=11, n = 100-88/3 = 4

 

As you can see, as x increases, n decreases.

 

So, the maximum number of child tickets of 28 results when the adult ticket price is $9, with each child ticket priced at $1.

 

NOTE: The above is my understanding. I cannot say with certainty that my answer is correct!