Question

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

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

B. Large floats cost $600 to operate. The town has a budget of $2500 to operate the floats. How does this change your answer to part A? What combinations of large and small floats are possible?

I'm not getting this, especially part A. I need a system of inequalities, but I can't figure out how to set it up.

Answer 1

If there are x large and y small floats, then

x >= 1
y >= 1
30x+15y+10(x+y-1) >= 150

That is,
160 <= 40x+25y >= 200
or
32 <= 8x+5y <= 40

Work similarly for part B.

Answer 2

But we are doing systems of linear inequalities, so I'd want at least two different inequalities. Also, I don't understand how you put x,y, and -1 into the parentheses. Also, would this work?

30x + 15y >= 150

x + y - 10 <= 200

Answer 3

you have to put 10' of space between floats, so if there are 12 floats, the length includes 11 "in-between" spaces of 10' each.

YES! Good catch. I forgot to account for the maximum length of 200'

But you still have to include the spaces in your inequalities.

Answer 4

How can I include those spaces?

Answer 5

did you bother reading what I wrote?

multiply the number of spaces (x+y-1) by 10!

Answer 6

What would the system of inequalities be on part a. On that same question