I'm having trouble with this word problem, I need help bad can someone please help and explain. Its kind of long. Can someone help me within the hour I'm desperate. Thanks
Here's the problem:
The PTO of Parksville Elementary School is having a Bazaar and all of the classes are expected to contribute to this fun and exciting event. The third grade teachers , along with some dedicated parents(e.g. YOU!), decide to sell cotton candy. A little research shows you can get the machine for $40, cleaning supplies will cost $10. The sugar/cone combo packages that cost $10 each will serve 100. The committee thinks they could probably sell 180 of these puffy globs of goodness, so they order two packages. (Note: You can get a refund for unopened packages--so only open them as needed). One of the parents asks: If we sell the cotton candy $1.50 each, how many servings must be sold to break even? You have volunteered to create the equations and graph the cost analysis chart so you will be able to answer that question, as well as the following questions:
a. What are the Cost equations? Graph these equations.
b. What is the Revenue equation? Graph this equation.
c. Where do these two lines cross? (Where is the Break-Even point?)
d. Profit equals Revenue minus Costs (P=R-C). What are the Profit equations?
e. How much profit will be made if 99 cones are sold?
f. What's the profit if 102 cones are sold? Do you always make more by selling more?
g. How much profit will be made if 150 servings are sold?
h. If the committee wants to make $300, how many cones must be sold? Can you do it?
i. How much would you have to sell each cone for to make a profit of $300 w/o getting extra supplies?
They sure make "word problems" harder by putting in so many words. Yours reads like a Jane Austen novel.
I suggest you let x be the number of cones sold.
a. For the cost equation, if you sell 100 or less, the cost is
C(x) = 50 + 10 = 60
If you sell 101 to 200, the cost is
C = 70 (since new box of 100 must be openied)
If you sell 201 to 300, the cost is C= 80, etc.
The cost function looks like a flight of stairs. You draw it.
b. The Revenue equation is
R = 1.5 X ($1.50 per cone)
c. You can make break even by selling less than 101.
Just set R = 1.5 X = 60 and solve for X
d. I have already told you what C anr r look like. You plot R
e. For 99 cones,
P = 99 x 1.5 - 60 = $88.50
f. For 102 cones,
P = 102 x 1.5 - 70 = $83.00
Use similar logic for g and h
i. I assume that "without getting extra supplies" means selling 200 cones. Allowing for a differnt selling price P, the profit (if you sell them all)would be
P*200 - 70 = 300
200 P = 370
P = $1.85
To solve this word problem, we need to break it down into several steps.
Step 1: Define the variables.
Let x be the number of cotton candy cones sold.
Step 2: Determine the cost equation.
The cost of selling cotton candy depends on the number of cones sold. We need to consider the cost of the machine, cleaning supplies, and the sugar/cone combo packages.
- If you sell 100 or fewer cones, the cost is $60 (machine cost + cleaning supplies).
- If you sell 101 to 200 cones, the cost is $70 (machine cost + cleaning supplies + cost of opening a new sugar/cone combo package).
- If you sell 201 to 300 cones, the cost is $80, and so on.
The cost equation can be represented as follows:
C(x) = 50 + 10 * (⌈x/100⌉ - 1), where ⌈x/100⌉ represents the ceiling function that rounds up to the nearest whole number.
Step 3: Determine the revenue equation.
The revenue from selling cotton candy depends on the number of cones sold and the selling price per cone, which is $1.50.
The revenue equation can be represented as follows:
R(x) = 1.5 * x, where x is the number of cones sold.
Step 4: Find the break-even point.
To find the break-even point, we need to find the number of cones sold at which the revenue is equal to the cost.
Set R(x) = C(x) and solve for x:
1.5 * x = 50 + 10 * (⌈x/100⌉ - 1)
By solving this equation, you can find the value of x where the revenue equals the cost, which is the break-even point.
Step 5: Calculate the profit.
The profit equation can be calculated by subtracting the cost from the revenue:
P(x) = R(x) - C(x)
Step 6: Answer the specific questions.
Using the equations and calculations, you can now answer the specific questions in the word problem.
- For question e: Substitute x = 99 into the profit equation P(x) to find the profit when 99 cones are sold.
- For question f: Substitute x = 102 into the profit equation P(x) to find the profit when 102 cones are sold.
- For question g: Substitute x = 150 into the profit equation P(x) to find the profit when 150 cones are sold.
- For question h: Set P(x) equal to $300 and solve for x to find the number of cones that must be sold to make a profit of $300.
- For question i: Set P(x) equal to $300, assuming that extra supplies are not needed, and solve for x to find the selling price per cone that would result in a profit of $300 without purchasing extra supplies.
By following these steps and using the equations provided, you should be able to solve the word problem and answer each question accurately.