A town is organizing a Fourth of July Parade.

Question

A town is organizing a Fourth of July parade. There will be two sizes of floats in the parade, the first is 30ft and the second is 15ft.. A space of 10 ft will be left after each float.

A. Describe how the total length of the parade will be calculated.

B. The parade must be a least 150ft long, but less than 200ft long. What combinations of large and small floats are possible?

C. Large float costs $600 to operate. Small floats cost $300 to operate. The town has a budget of $2500 to operate the floats. How does this change your answers to part A? What combinations of large and small floats are possible?

Answer 1

A. If there is 10 ft of space after every float, and not just between them, then the total length is 40 ft per large float, and 25 ft per small float. Using this, you can write an equation for the total length.

B. Using the equation from part A, evaluate 150 ≤ L < 200. I would suggest for you to try checking the maximum number of both floats by imagining that only one size category existed, and fit it within 200 feet. Then slowly figure out the possible cases, remembering to be careful of the length constraints. L = 150 is fine, but L = 200 is not as the question says "less than" 200 ft and not "less than or equal to."

C. For this part, take your list of possible combinations from part B and just calculate the total costs for each. No need to redo previous work here. If the cost for one goes above $2500, then it is an invalid combination. From the surviving combinations, you can then more specifically tell what total lengths are possible, although the answer to part A remains the same.