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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Darrell's Bakery recently spent a total of on new equipment, and their average hourly operating costs are . Their average hourly receipts are . The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal? How many hours will that take?The bakery's expenses and receipts will both total _____ after _____ hours.
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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Darrell's Bakery recently spent a total of on new equipment, and their average hourly operating costs are . Their average hourly receipts are . The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal? How many hours will that take?The bakery's expenses and receipts will both total _____ after _____ hours.
- Define Variables: Let's define the variables:Let be the number of hours the bakery operates after buying the new equipment.The total expenses after hours will be the initial investment plus the operating costs, which is .The total receipts after hours will be the hourly receipts times the number of hours, which is .We want to find the value of when the expenses equal the receipts.
- Write Equation: Write the equation representing the situation where the expenses equal the receipts:
- Solve for x: Now, let's solve for x:Subtract from both sides to get:
- Calculate Total Expenses: So, the bakery will break even after hours.Now, we need to calculate the total expenses and receipts after hours.Total expenses = Initial investment + (Operating costs per hour Number of hours)Total expenses = + ( )
- Calculate Total Receipts: Calculate the total expenses:Total expenses = Total expenses = Total expenses =
- Calculate Total Receipts: Calculate the total expenses:Total expenses = Total expenses = Total expenses = Since the expenses and receipts are equal when the bakery breaks even, the total receipts will also be after hours.
