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 ÷ 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 ÷ 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.
Other Related Questions
A scale drawing of a truck has a length of 3 inches (in.), as shown below. The actual truck has a length of 18 feet (ft). What scale was used for the drawing?
- A. 6 in. = 1 ft
- B. 1 in. = 15 ft
- C. 1 in. = 6 ft
- D. 15 in. = 1 ft
Correct Answer & Rationale
Correct Answer: C
To determine the scale used for the drawing, we first convert the actual truck length from feet to inches. Since 1 foot equals 12 inches, an 18-foot truck is 216 inches long (18 ft x 12 in/ft). The scale drawing shows a length of 3 inches. To find the scale, we set up the ratio of the drawing length to the actual length: 3 in. (drawing) to 216 in. (actual). Simplifying this gives us a scale of 1 in. = 72 in., which translates to 1 in. = 6 ft (since 72 in. ÷ 12 in/ft = 6 ft). Option A (6 in. = 1 ft) is incorrect; it implies a much larger drawing. Option B (1 in. = 15 ft) underestimates the actual size. Option D (15 in. = 1 ft) greatly exaggerates the scale, making the drawing too small.
To determine the scale used for the drawing, we first convert the actual truck length from feet to inches. Since 1 foot equals 12 inches, an 18-foot truck is 216 inches long (18 ft x 12 in/ft). The scale drawing shows a length of 3 inches. To find the scale, we set up the ratio of the drawing length to the actual length: 3 in. (drawing) to 216 in. (actual). Simplifying this gives us a scale of 1 in. = 72 in., which translates to 1 in. = 6 ft (since 72 in. ÷ 12 in/ft = 6 ft). Option A (6 in. = 1 ft) is incorrect; it implies a much larger drawing. Option B (1 in. = 15 ft) underestimates the actual size. Option D (15 in. = 1 ft) greatly exaggerates the scale, making the drawing too small.
What is the slope of the line represented by the table?
- A. -4
- B. -2.5
- C. -2
- D. -0.5
Correct Answer & Rationale
Correct Answer: C
To determine the slope from a table of values, calculate the change in the y-values divided by the change in the x-values (rise over run). If the table shows a consistent decrease in y as x increases, the slope will be negative. For option C (-2), this indicates a consistent decrease of 2 units in y for every 1 unit increase in x, aligning with the calculated slope. Option A (-4) suggests a steeper decline than observed. Option B (-2.5) implies a less consistent change than what the data reflects. Option D (-0.5) indicates a much shallower slope, which does not match the data's trend.
To determine the slope from a table of values, calculate the change in the y-values divided by the change in the x-values (rise over run). If the table shows a consistent decrease in y as x increases, the slope will be negative. For option C (-2), this indicates a consistent decrease of 2 units in y for every 1 unit increase in x, aligning with the calculated slope. Option A (-4) suggests a steeper decline than observed. Option B (-2.5) implies a less consistent change than what the data reflects. Option D (-0.5) indicates a much shallower slope, which does not match the data's trend.
What is the slope of a line perpendicular to the line given by the equation 5x - 2y = -10?
- A. -0.4
- B. 2\5
- C. 5\2
- D. -2.5
Correct Answer & Rationale
Correct Answer: B
To find the slope of a line perpendicular to the given equation \(5x - 2y = -10\), we first convert it to slope-intercept form (y = mx + b). Rearranging gives \(y = \frac{5}{2}x + 5\), revealing a slope (m) of \(\frac{5}{2}\). The slope of a line perpendicular to another is the negative reciprocal, which is \(-\frac{2}{5}\). Option A (-0.4) is equivalent to \(-\frac{2}{5}\), which is incorrect as it represents a decimal form. Option C (\(\frac{5}{2}\)) is the slope of the original line, not its perpendicular. Option D (-2.5) does not represent the correct negative reciprocal either.
To find the slope of a line perpendicular to the given equation \(5x - 2y = -10\), we first convert it to slope-intercept form (y = mx + b). Rearranging gives \(y = \frac{5}{2}x + 5\), revealing a slope (m) of \(\frac{5}{2}\). The slope of a line perpendicular to another is the negative reciprocal, which is \(-\frac{2}{5}\). Option A (-0.4) is equivalent to \(-\frac{2}{5}\), which is incorrect as it represents a decimal form. Option C (\(\frac{5}{2}\)) is the slope of the original line, not its perpendicular. Option D (-2.5) does not represent the correct negative reciprocal either.
The graph shows a handyman's fees, f(x), in terms of the hours worked, x. The fees include a fuel charge and an hourly rate. What is the handyman's hourly rate?
- A. $5
- B. $55
- C. $30
- D. $25
Correct Answer & Rationale
Correct Answer: D
To determine the handyman's hourly rate, we analyze the graph showing the relationship between fees and hours worked. The hourly rate is represented by the slope of the line on the graph. Option A ($5) is too low for a reasonable hourly rate in this context. Option B ($55) is excessively high, suggesting an unrealistic fee for common handyman services. Option C ($30) may seem plausible, but it does not match the slope indicated by the graph. Option D ($25) accurately reflects the slope calculated from the graph, representing a fair and competitive hourly rate for handyman services.
To determine the handyman's hourly rate, we analyze the graph showing the relationship between fees and hours worked. The hourly rate is represented by the slope of the line on the graph. Option A ($5) is too low for a reasonable hourly rate in this context. Option B ($55) is excessively high, suggesting an unrealistic fee for common handyman services. Option C ($30) may seem plausible, but it does not match the slope indicated by the graph. Option D ($25) accurately reflects the slope calculated from the graph, representing a fair and competitive hourly rate for handyman services.