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 L = number of larger 30 foot floats, let S = number of smaller 15 foot floats

the parade length = 30L + 15S = 10(L+S-1) = 30L+15S + 10L+10S -1 = 40L+25S -1

P = 40L+25S -1

150<40L+25S-1<200

151<40L+25S < 201

151/5< 8L + 5S < 201/5 or

30.2 < 8L + 5S < 40.2

L<5, S<8

0<600L + 300S < 2500

0< 6L+3S < 25

L<4, S<8

the cost constraint limited large floats to 4 instead of 5, without the cost constraints.

small floats are no more than 8, regardless of the cost constraints.

8(300)=2400, but a 9th small float would make 2700>budget allowed

4(600) =2400, but a 5th large float would make 3000> budget

6L+3S<25

either L=0, S=8

L=1, S=6

L=2, S= 4

L=3, S=2

or L=4, S=0

5 possibilities that meet the budget restraints and parade length maximums

but 30.2 < 8L:+5S allows for four more possibilities

L=0, S=7

L=1, S=5

L=2, S =3

L=3, S= 2

any lesser combinations would be too short for the parade length minimum