A town is organizing a parade. There will be floats of only 2 sizes, 30ft. and 15ft. A space of 10 ft. will be left after each float.
a. the parade must be at least 150 feet long, but less than 200ft long. what is the combinations of large and small floats are possible?
b. Large floats cost $600 to operate. Small floats cost $300 to operate. The town has a budget of $2500 to operate floats. what combinations of large and small floats are possible?
Please help! Thank you
To solve both parts of the problem, we need to find the possible combinations of 30ft. and 15ft. floats that satisfy the given conditions. We can approach this problem by using algebraic equations.
a. The length of the parade with floats can be expressed as:
Length = (30ft. + 10ft.) * number of large floats + (15ft. + 10ft.) * number of small floats
We know that the maximum length of the parade is 200ft., so we can write the inequality:
(30 + 10) * number of large floats + (15 + 10) * number of small floats < 200
Simplifying the inequality:
40 * number of large floats + 25 * number of small floats < 200
To find the combinations of floats, we can try different values for the number of large floats and calculate the corresponding number of small floats that satisfy the inequality and make the parade length within the given range (150ft. to 200ft.).
Here are some possible combinations:
- For 1 large float:
- 40 * 1 + 25 * 4 = 160ft. (within the range)
- For 2 large floats:
- 40 * 2 + 25 * 3 = 170ft. (within the range)
- 40 * 2 + 25 * 4 = 195ft. (within the range)
- For 3 large floats:
- 40 * 3 + 25 * 2 = 170ft. (within the range)
- 40 * 3 + 25 * 3 = 195ft. (within the range)
- 40 * 3 + 25 * 4 = 220ft. (not within the range)
So, the possible combinations of large and small floats that satisfy the given conditions are:
- 1 large float and 4 small floats
- 2 large floats and 3 small floats
- 2 large floats and 4 small floats
- 3 large floats and 2 small floats
- 3 large floats and 3 small floats
b. To find the combinations of large and small floats that fit within the budget of $2500, we can use a similar approach.
The cost of operating floats can be expressed as:
Cost = $600 * number of large floats + $300 * number of small floats
We know that the budget is $2500, so we can write the inequality:
$600 * number of large floats + $300 * number of small floats <= $2500
To find the combinations of floats within the budget, we can try different values for the number of large floats and calculate the corresponding number of small floats that satisfy the inequality.
Here are some possible combinations:
- For 1 large float:
- $600 * 1 + $300 * 7 = $2700 (not within the budget)
- For 2 large floats:
- $600 * 2 + $300 * 4 = $2400 (within the budget)
So, the only possible combination of large and small floats that fits within the budget is:
- 2 large floats and 4 small floats
Note: These are just a few examples of possible combinations; there may be more combinations that satisfy the given conditions.