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.
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.
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
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.
How can I include those spaces?
did you bother reading what I wrote?
multiply the number of spaces (x+y-1) by 10!
What would the system of inequalities be on part a. On that same question
To solve part A, we need to set up a system of inequalities based on the given information. Let's denote the number of large floats as L and the number of small floats as S.
1. The length of each large float is 30 ft, and the length of each small float is 15 ft. Considering there is a space of 10 ft left after each float, the total length of the parade can be calculated as:
Total Length = Length of Large Floats + Length of Small Floats + Spaces
Total Length = 30L + 15S + 10(L + S)
2. The parade must be at least 150 ft long, so the inequality is:
30L + 15S + 10(L + S) ≥ 150
3. The parade's length should be less than 200 ft, so the inequality is:
30L + 15S + 10(L + S) < 200
To summarize, the system of inequalities for part A is:
30L + 15S + 10(L + S) ≥ 150
30L + 15S + 10(L + S) < 200
To solve this system of inequalities and find the possible combinations of large and small floats, you can graph the solution set or use algebraic methods such as substitution or elimination.