prealgebra

Question

Hi again, there are a couple of questions I'm stuck on and I was wondering if anyone could help?
Here's the word problem- The local swim center is making a special offer. They usually charge $7 per day to swim at the pool. This month swimmers can pay an enrollment fee of $30 and then the daily pass will only be $4 per day. 

Now, question 5 is asking: Supposed you do not take the offer. Write an equation that represents the amount of money (m) you would spend based on how many days you go to the pool (d) if the passes were bought at full price.

Question 6 is one i'm also stuck on. It's: Write a second equation that represents the amount of money you would spend if you decided to take the special offer.


If anyone could take a few minutes out of their day to help me that would be great. :) Thank you!

Answer 1

Let x = the number of days you decide to swim at the pool that month.  If it costs $7 each day you swim, your cost would be:

 

Cost = $7*x = 7x

 

Now let's suppose you take the swim center's offer.  You pay $30 one time and $4 each day you swim, so your cost would be:

 

Cost = $30 + $4*x = 30 + 4x

 

The costs are equal when:

 

7x = 30 + 4x

3x = 30

x = 10 days

 

So if you swim 10 days the costs are equal.  If you swim less than 10 days, it's cheaper to NOT to buy the swim club's offer.  If you swim MORE than 10 days, it's cheaper if you take the swim club's offer.