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Are you considering a season of fun at the city pool but torn between the special offer and the standard rate? Irene's question might just resonate with you. How many visits does it take for the special offer to be truly worth it? Let's dive into the numbers and find out.
Imagine this: the city pool rolls out a tantalizing summer deal. For an initial $20 fee, you get unlimited access to the pool for just $4 per day. Sound good? Well, hold on. The standard rate without the special offer is $8 per day. So, when does this special deal become a better option?
Let's denote the number of visits to the pool as N. Now, how do we represent the cost of the special deal mathematically? It's simple. You pay $20 upfront, plus $4 for each day you visit. So, the total cost for the special deal is 20 + 4N.
What about the standard rate? No upfront cost, just $8 per day. Thus, the total cost for the standard rate is 8N.
To determine when the special offer is a better deal, we need to set up an inequality. The special offer is better when the cost of the special deal is less than the cost of the standard rate. Mathematically, this is represented as:
20 + 4N < 8N
Now, the fun part begins. Simplifying this inequality, we subtract 4N from both sides, which gives us:
20 < 4N
Divide both sides by 4, and we get:
5 < N
This inequality tells us that after 5 visits, the special offer becomes a better deal. Why? Because the upfront cost of $20 plus the daily cost of $4 for 5 days equals $40, which is less than the $40 you would spend at the standard rate for the same number of visits.
So, if you're planning to visit the pool more than 5 times this summer, the special offer is the way to go. Otherwise, you might want to stick with the standard rate. Irene's question has opened up a world of mathematical reasoning, proving that sometimes, the numbers can guide us to the best summer fun.
Are you ready to splash into savings? How many times do you think you'll visit the pool this summer? Let us know in the comments and share this article with fellow pool enthusiasts to help them make their decision!
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