A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00 but cost the school $2.00 to prepare. After all expenses were paid, the school raised $2,400 at the fundraiser. Which equation can be used to find x, the number of plates that were sold? Set up the cost equation C(x) where x is the number of plates sold: C(x) = Cost per plate * x plates C(x) = 2x Set up the revenue equation R(x) where x is the number of plates sold: R(x) = Sales price per plate * x plates C(x) = 8x Set up the profit equation P(x) where x is the number of plates sold: P(x) = R(x) - C(x) P(x) = 8x - 2x P(x) = 6x We're told the profits P(x) for the fundraiser were $2,400, so we set 6x equal to 2400 and solve for x: 6x = 2400 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3D2400&pl=Solve']type it in our math engine[/URL] and we get: x =[B]400 plates[/B]

A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. The company sells each bear for $12.00 each. How many bears must this company sell in order to break even? [U]Set up the cost function C(b) where b is the number of bears:[/U] C(b) = Cost per bear * b + factory expenses C(b) = 8b + 1500 [U]Set up the revenue function R(b) where b is the number of bears:[/U] R(b) = Sale Price per bear * b R(b) = 12b [U]Break-even is where cost equals revenue, so we set C(b) equal to R(b) and solve for b:[/U] C(b) = R(b) 8b + 1500 = 12b To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B1500%3D12b&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]375[/B]

Alana puts $700.00 into an account to use for school expenses. The account earns 8% interest, compounded annually. How much will be in the account after 4 years? We use our [URL='https://www.mathcelebrity.com/compoundint.php?bal=700&nval=8&int=4&pl=Annually']balance with interest calculator[/URL] and we get: [B]$958[/B]

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Hunter puts $300.00 into an account to use for school expenses. The account earns 15% interest, compounded annually. How much will be in the account after 10 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=300&nval=10&int=15&pl=Annually']compound interest calculator[/URL], we get: [B]$1,213.67[/B]

Jay earns S amount per day for working in a company. His total expenses per day is equal to the amount E. Write an expression to show how much he earned per day in a month. Suppose he is working for 20 days per month. [LIST=1] [*]Each day, Jay earns a profit of S - E. [*]For one month (30 days), he earns 30(S - E) [*]For 20 working days in a month, he earns 20(S - E) [/LIST]

Joey puts $1,000.00 into an account to use for school expenses. The account earns 12% interest, compounded annually. How much will be in the account after 6 years? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=1000&nval=6&int=12&pl=Annually']balance calculator[/URL], we get [B]$1,973.82[/B]

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month? Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is: C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have: C(x) = 264 The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns. Now, profit is Revenue - Cost. Our profit function is: P(x) = 53x - 264 To make a profit of $800 per month, we set P(x) = 800. 53x - 264 = 800 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=53x-264%3D800&pl=Solve']equation solver[/URL], we get: [B]x ~ 21 lawns[/B]

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point. Calculate the revenue function R(c) where s is the number of sodas sold: R(s) = Sale Price * number of units sold R(s) = 50s Calculate the cost function C(s) where s is the number of sodas sold: C(s) = Variable Cost * s + Fixed Cost C(s) = 0.25s + 900 Our break-even point is found by setting R(s) = C(s): 0.25s + 900 = 50s We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]18.09[/B]

Stacy sells art prints for $12 each. Her expenses are $2.50 per print, plus $38 for equipment. How many prints must she sell for her revenue to equal her expenses? Let the art prints be p Cost function is 38 + 2p Revenue function is 12p Set cost equal to revenue 12p = 38 + 2p Subtract 2p from each side 10p = 38 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=10p%3D38&pl=Solve']equation calculator[/URL] gives us [B]p = 3.8[/B]