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Notes
Questions
\(\textbf{1)}\) A printing machine costs \($450\), it costs \($21\) to make a shirt. And the shirts sell for \($30\). Including the price of the printing machine, how many shirts must you sell to break even?
\(\textbf{2)}\) Sarah starts a bakery and invests $10000 in equipment and supplies. She sells each loaf of bread for $3, and the cost of ingredients for each loaf is $0.50. How many loaves of bread does Sarah need to sell to break even?
\(\textbf{3)}\) David starts a lawn care business and invests $2250 in equipment. He charges $50 for each lawn he mows, and the cost of supplies for each lawn is $5. How many lawns does Tom need to mow to break even?
\(\textbf{4)}\) Jen starts a tutoring business and invests $2600 in marketing and supplies. She charges $70 per hour for her services, and the cost of materials for each session is $5. How many hours of tutoring does Rachel need to provide to break even?
\(\textbf{5)}\) Bryn starts a pet grooming business and invests $560 in equipment and supplies. She charges $30 for each grooming service, and the cost of supplies for each service is $2. How many grooming services does Alex need to provide to break even?
\(\textbf{6)}\) Michael starts a home cleaning business and invests $1870 in supplies and marketing. He charges $100 for each cleaning service, and the cost of supplies for each service is $15. How many cleaning services does Maria need to provide to break even?
\(\textbf{7)}\) Two car rental companies charge the following values for x miles.
Car Rental A: \(y=3x+150 \,\,\)
Car Rental B: \(y=4x+100\)
For how many driven miles is the cost of the two companies the same?
See Related Pages\(\)
\(\bullet\text{ Word Problems- Linear Equations}\)
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\(\bullet\text{ Word Problems- Averages}\)
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\(\bullet\text{ Word Problems- Consecutive Integers}\)
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\(\bullet\text{ Word Problems- Distance, Rate and Time}\)
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\(\bullet\text{ Word Problems- Break Even}\)
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\(\bullet\text{ Word Problems- Ratios}\)
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\(\bullet\text{ Word Problems- Age}\)
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\(\bullet\text{ Word Problems- Mixtures and Concentration}\)
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In Summary…
Break-even analysis is a financial tool that helps businesses determine the point at which their revenue is equal to their costs. At this point, the business is said to be “breaking even,” as it is not making a profit or loss.
To determine the break-even point, a business must first identify its fixed costs, which are expenses that do not vary based on the number of units produced or sold. These may include rent, salaries, and insurance. The business must also determine its variable costs, which are expenses that do vary based on the number of units produced or sold. These may include raw materials, commissions, and shipping.
Break-even analysis is useful for businesses because it helps them determine the minimum sales volume needed to cover their costs. If a business knows that it needs to sell a certain number of units to break even, it can make informed decisions about pricing, production, and marketing.
Break-even analysis can also be used to compare different products or business models. For example, a business might use break-even analysis to decide whether to manufacture a product in-house or outsource production to a third party.
There are several limitations to break-even analysis, however. It assumes that all costs and revenues are constant, which may not always be the case. It also does not account for the time value of money, which is the idea that money is worth more today than it is in the future. Despite these limitations, break-even analysis is a valuable tool for businesses looking to understand their financial performance and make informed decisions.
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