Problem 9-60

Algeria has decided to take put an advertisement in the U.N. newspaper, Liberty Daily. The newspaper charges a base fee of $1200 for an ad. There is and additional fee of $300 for every inch in height. If Algeria is willing to spend any amount up to (and including) $2700, what choices does the country have for the height of the ad?

What we know:                                                                                                                                                                          

-the base fee is $1200                                                                                                                                                               

-there is an additional $300 fee for every inch of height added                                                                                          

-Algeria’s “budget” is $2700                                                                                                                                                  

Work for problem 9-60

How we solved it:

1. First we looked at the problem and broke down the problem. We organized the information that we from the problem and found out that we can't go over the $2700 that is the budget Algeria has put aside for the ad. Using this organization tactic helped us figure out the problem after because we were able to see the information and understand what the equation would look like. So far there has been no math used and we already know a lot about the problem.

2. Next we looked at what the problem was asking and took and understanding of what the problem is asking and the goal of the problem. The goal of this problem is to figure out potential height of the ad. Now that we know the goal we are able to set up the equation (which we already know by looking that the information) and solve the problem to find out how much height in inches Algeria is able to add onto their ad.

3. In order to solve this problem and find the potential height of the ad, first we have to create an equation. the equation was very simple and as said before we are able to tell what the equation will look like by just looking that the information written down above and below in the work shown. The equation is 1200+300x=2700. The 1200 represents the base fee, the 300 is the additional fee for every inch of height added and the 2700 is Algeria's set budget.

4. Once we wrote down the equation and understood the equation and problem we had to take the final step of solving. To solve this equation first we must remove the 1200 from the problem because that is our base fee and we want to simplify the problem as much as we can to be able to get the x which is the $300 additional fee alone. So once we subtract 1200 from both sides, creating the new equation of 300x=1500 and having it be very simplified now and our x being alone we now solve for x. Now to be able to find what x is we then divide both sides by 300 giving us our answer. The answer is x=5 inches and 5 inches is the max amount of height for the ad is 5 inches. This would use all of Algeria's money set aside for the ad and give them the max amount if extra inches they can use for the ad. Lastly we have to change we x=5 to an inequality so it can be placed on a number line, that inequality is: x ≤ 5

Conclusion:

If Algeria wants to have the max amount of inches on their ad the max amount of inches that can be used are 5 inches. 5 is the max amount because 300 divided by 1500 is 5 and Algeria's budget is $2700, however we already removed the base fee of 1200 from the 2700 which gave us the 1500. Now the 300 is the additional fee for every inch added and if Algeria were to add 5 more inches onto the ad then Algeria will use the entire $2700 for their budget.