A town is organizing a Fourth of July Parade. Solve the Problem by showing your work, solutions and your steps.

Question

Solve the Problem by showing your work, solutions and your steps.

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 B? What combinations of large and small floats are possible?

Answer 1

Let the large float be L and the small float be S

There are 10 ft behind each float except for the last one.

a) 30L + 10L + 15S + 10S - 10 = 40L + 25S - 10

b) Label points (L, S)

We can think of a lot of shortcuts, but we see that solutions will have L ranging from 0 to 5 and then finding what values of S solve the equation, as 40L - 10 <= 200 means 40L <= 210, or L <= 5

L = 0. 150 <= 25S - 10 <= 200 160 <= 25S <= 210 S = 7, 8

L = 1. 150 <= 25S + 40 - 10 <= 200 120 <= 25S <= 170 S = 5, 6

L = 2. 150 <= 25S + 80 - 10 <= 200 80 <= 25S <= 130 S = 4, 5

L = 3. 150 <= 25S + 120 - 10 <= 200 40 <= 25S <= 90 S = 2, 3

L = 4. 150 <= 25S + 160 - 10 <= 200 0 <= 25S <= 50 S = 0, 1, 2

L = 5. 150 <= 25S + 200 - 10 <= 200 -40 <= 25S <= 10 S = 0

Solutions: (0, 7), (0, 8), (1, 5), (1, 6), (2, 4), (2, 5), (3, 2), (3, 3), (4, 0), (4, 1), (4, 2), (5, 0)

The budget is $2500. Floats are $300 for small and $600 for the large. Thus, append this to the values above.

(0, 7, 2100), (0, 8, 2400), (1, 5, 2100), (1, 6, 2400), (2, 4, 2400), (2, 5, 2700), (3, 2, 2400), (3, 3, 2700), (4, 0, 2400), (4, 1, 2700), (4, 2, 3000), (5, 0, 3000)

Feasible solutions have cost less than or equal to $2500

(0, 7, 2100), (0, 8, 2400), (1, 5, 2100), (1, 6, 2400), (2, 4, 2400), (3, 2, 2400), (4, 0, 2400)