Answer:
p ≤ 8
Explanation:
Let's go over what we know that can help us build an inequality:
we know that these friends can spend no <em>more </em>than $325, meaning that they can either spend exactly $325, or they could spend less. This is our first clue, that one side of the inequality will be 325, and that the inequality sign will be <em>less than or equal to </em>( ≤ ) :
amount spent ≤ 325
Now, we want to figure out how many people can go (p)--but there's something we need to consider first--the parking.
Assuming that all friends take one car, we know we will have 11 dollars less to spend on admission (you can write this two ways).
amount spent on tickets + 11 ≤ 325
or, we can simplify it:
amount spent on tickets + 11 ≤ 325
- 11 -11
amount spent on tickets ≤ 314
(I will be using the second way, you could always plug it back into the first way though)
now, we know that each "p" that we include will be multiplied by 39.25
<em>Why? Imagine we have one p (one person), they will cost 39.25, so we could write that as (p · 39.25) , ( 1· 39.25 ) -- we use × because that's how many </em><em>times</em><em> we're adding the number. If we have two p, we could write it as (2p · 39.25)--there's an easier way to do this though</em>
<em />
So, we can write "p" to stand for all possible values of p possible,
p · 39.25 ≤ 314 (we write this slightly differently):
39.25p ≤ 314
Now, let's simplify!
39.25p ≤ 314
÷ 39.25 ÷ 39.25 (divide by 39.25 to isolate p)
p ≤ 8
So, we know that the number of friends admitted must be less than or equal to 8, expressed as:
p ≤ 8
hope this helps! let me know if you need clarification on anything :)
