A town is organizing a Fourth of July parade.There will be two sizes of floats in the parade, as shown below. A space of 10ft 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?

Question

A town is organizing a Fourth of July parade.There will be two sizes of floats in the parade, as shown below. A space of 10ft 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?

anonymous · Answer

a. 
150 < 15S + 30L + 10(S+L-1) < 200 
150 < 25S + 40L - 10 < 200 

1: 165= 7 small and 0 large 
2: 190= 8 small and 0 large 
3: 155= 5 small and 1 large 
4: 180= 6 small and 1 large 
5: 170= 4 small and 2 large 
6: 195= 5 small and 2 large 
7: 160= 2 small and 3 large 
8: 185= 3 small and 3 large 
9: 150= 0 small and 4 large 
10: 175= 1 small and 4 large 
11: 200= 2 small and 4 large 
12: 190= 0 small and 5 large 


b. 
600L + 300S < 2500 
1: 165= 7 small and 0 large 
2: 190= 8 small and 0 large 
3: 155= 5 small and 1 large 
4: 180= 6 small and 1 large 
5: 170= 4 small and 2 large 
6: 160= 2 small and 3 large 
7: 150= 0 small and 4 large