The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie.
The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price.
The shop owner needs to determine the total daily cost of making x cookies. Which of the following linear equations represents the cost, C, in dollars?
- A. C=4.6x+995
- B. C=0.046x+2
- C. C=0.19x+41.26
- D. C=1.2x+212.26
Correct Answer & Rationale
Correct Answer: C
The equation representing total daily cost must account for both fixed and variable costs. The fixed cost of $41.26 reflects the shop's expenses, while the variable cost is $0.19 per cookie, leading to the term 0.19x for x cookies. Therefore, C = 0.19x + 41.26 accurately captures both components. Option A incorrectly suggests a much higher fixed cost and variable rate, implying unrealistic expenses. Option B has a fixed cost that is too low and a variable cost that is also incorrect. Option D presents exaggerated figures for both fixed and variable costs, misrepresenting the shop's actual expenses.
The equation representing total daily cost must account for both fixed and variable costs. The fixed cost of $41.26 reflects the shop's expenses, while the variable cost is $0.19 per cookie, leading to the term 0.19x for x cookies. Therefore, C = 0.19x + 41.26 accurately captures both components. Option A incorrectly suggests a much higher fixed cost and variable rate, implying unrealistic expenses. Option B has a fixed cost that is too low and a variable cost that is also incorrect. Option D presents exaggerated figures for both fixed and variable costs, misrepresenting the shop's actual expenses.
Other Related Questions
The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie.
The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price.
The owner has decided to take out a loan to purchase updated equipment. A bank has agreed to loan the owner $2,000 for the purchase of the equipment at a simple interest rate of 4.69% payable annually.
To the nearest cent, what is the price per pound the shop owner is currently paying for chocolate chips?
- A. $0.10
- B. $4.38
- C. $0.23
- D. $4.28
Correct Answer & Rationale
Correct Answer: D
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
Kelly has a home business making jewellery. It takes 2 hours for her to make each bracelet and 3.5 hours to make each necklace. Next month she plans to spend 140 hours to make jewellery. If she fills a special order for 22 bracelets at the beginning of the mouth and spends the rest of the month making necklaces, how many necklaces can Kelly make in the month
- A. 52
- B. 27
- C. 40
- D. 31
Correct Answer & Rationale
Correct Answer: B
To determine how many necklaces Kelly can make, first calculate the time spent on bracelets. Making 22 bracelets takes 22 x 2 = 44 hours. Subtracting this from her total available time of 140 hours leaves her with 140 - 44 = 96 hours for necklaces. Each necklace takes 3.5 hours, so she can make 96 รท 3.5 = 27.43, which rounds down to 27 necklaces since she cannot make a fraction of a necklace. Options A (52), C (40), and D (31) are incorrect because they exceed the available time after accounting for the hours spent on bracelets, indicating miscalculations in time management or misunderstanding of the problem constraints.
To determine how many necklaces Kelly can make, first calculate the time spent on bracelets. Making 22 bracelets takes 22 x 2 = 44 hours. Subtracting this from her total available time of 140 hours leaves her with 140 - 44 = 96 hours for necklaces. Each necklace takes 3.5 hours, so she can make 96 รท 3.5 = 27.43, which rounds down to 27 necklaces since she cannot make a fraction of a necklace. Options A (52), C (40), and D (31) are incorrect because they exceed the available time after accounting for the hours spent on bracelets, indicating miscalculations in time management or misunderstanding of the problem constraints.
What is the value of 0.6 - (0.7)(1.4)?
- A. -0.38
- B. -0.14
- C. -0.42
- D. -1.5
Correct Answer & Rationale
Correct Answer: A
To solve 0.6 - (0.7)(1.4), first calculate the product (0.7)(1.4), which equals 0.98. Subtracting this from 0.6 gives 0.6 - 0.98 = -0.38. Option B (-0.14) results from an incorrect subtraction, possibly miscalculating the product. Option C (-0.42) suggests an error in understanding the subtraction process, likely misapplying the negative sign. Option D (-1.5) is far too low and indicates a misunderstanding of basic arithmetic operations. Thus, the correct calculation leads to -0.38, confirming option A as the accurate answer.
To solve 0.6 - (0.7)(1.4), first calculate the product (0.7)(1.4), which equals 0.98. Subtracting this from 0.6 gives 0.6 - 0.98 = -0.38. Option B (-0.14) results from an incorrect subtraction, possibly miscalculating the product. Option C (-0.42) suggests an error in understanding the subtraction process, likely misapplying the negative sign. Option D (-1.5) is far too low and indicates a misunderstanding of basic arithmetic operations. Thus, the correct calculation leads to -0.38, confirming option A as the accurate answer.
A diver jumps from a platform. The height, h meters, the diver is above the water t seconds after jumping is represented by h = -16t^2 + 16t + 6.5. To the near hundredth of a second, how many seconds after jumping is the diver 2.5 meters above the water?
- A. 2.79
- B. 1.32
- C. 2.83
- D. 1.21
Correct Answer & Rationale
Correct Answer: D
To find when the diver is 2.5 meters above the water, substitute h = 2.5 into the equation: \[ 2.5 = -16t^2 + 16t + 6.5. \] Rearranging gives: \[ -16t^2 + 16t + 4 = 0. \] Using the quadratic formula, we solve for t, yielding two potential solutions. The option D (1.21 seconds) is valid as it falls within the realistic time frame of the jump. Options A (2.79) and C (2.83) exceed the expected time of descent, while B (1.32) does not satisfy the equation, confirming that only D accurately represents the diver's position at 2.5 meters above the water.
To find when the diver is 2.5 meters above the water, substitute h = 2.5 into the equation: \[ 2.5 = -16t^2 + 16t + 6.5. \] Rearranging gives: \[ -16t^2 + 16t + 4 = 0. \] Using the quadratic formula, we solve for t, yielding two potential solutions. The option D (1.21 seconds) is valid as it falls within the realistic time frame of the jump. Options A (2.79) and C (2.83) exceed the expected time of descent, while B (1.32) does not satisfy the equation, confirming that only D accurately represents the diver's position at 2.5 meters above the water.