Instructions Think of an activity that you enjoy or are interested in. Some examples are reading, swimming, or leveling up your gaming character. Use your activity to work through the following problems: Create a scenario that leads to an inequality of the form ax + b > c. You can use any of the inequality symbols (>, ≥, <, ≤) in your inequality. For this step, just write the word problem. Write the inequality and show all work to solve the inequality. Graph the solution to your inequality on a number line. Explain what your solution means in the context of the 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.

Let m represent the amount of money you spend, and let d represent the number of days you go to the pool. At full price, you would spend $7 per day, so m=7d represents the amount of money you would spend without the special offer.

Again, let m represent the amount of money you spend, and let d represent the number of days you go to the pool. With the special offer, you would spend $30 once, and then $4 per day, so m=4d+30 represents the amount of money you would spend with the special offer.

We can graph these equations on the same set of axes: graph at the bottom

When considering when the special offer will become a better deal, we want to find out after how many days we will be spending less money than with the full price passes. For example, after 3 days, the full price offer will cost us $21 dollars and the special offer will cost us $39, so the special will cost more. We see that this is because of the initial fee of $30.

Algebraically, we can determine exactly when the special offer costs the same amount as the standard price by setting our two expressions for m equal to each other and solving for d.

4d+30=7d

30=3d

d=10.

So, when d=10, or on the 10th day, the special offer and the original will have cost us the same amount of money:

m=7(10)=70

and

m=4(10)+30=70.

Because on the 11th day, and every day thereafter, the special offer will cost less ($4 a day versus $7 a day), we can conclude that after the 10th day is when the special offer becomes a better deal.

Graphically, we can see that the graph of the special offer drops below the graph of the original offer after d=10, and as lower translates into less money spent, we can see our conclusion in the graph, as well.

We have a total of $60 to spend, and so m=60. We can substitute this into the equation for each offer.

Special offer:

60=4d+30⟹30=4d⟹304=7.5=d

Since d represents days, and we can only go for full days, .5 of a day does not make sense, and so we find that with $60, we can go to the pool for 7 days if we take the special offer.

Original offer:

60=7d⟹607=847=d

Again, we cannot visit the swim center for 47 of a day, and so with $60 we are able to go for a full 8 days if we take the full price offer.

Therefore, we should take the original offer if we only have $60 to spend, because we can go for an additional day over the special offer.

Step-by-step explanation: