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
The radius of the sphere below is 6 centimeters (cm). What is the volume, in cubic centimeters, of the sphere?
- A. 904.32
- B. 150.72
- C. 25.12
- D. 75.36
Correct Answer & Rationale
Correct Answer: A
To find the volume of a sphere, the formula \( V = \frac{4}{3} \pi r^3 \) is used, where \( r \) is the radius. For a radius of 6 cm, the calculation is: \[ V = \frac{4}{3} \pi (6)^3 = \frac{4}{3} \pi (216) \approx 904.32 \, \text{cm}^3 \] Option A (904.32) correctly represents this volume. Option B (150.72) and Option C (25.12) are significantly lower than the actual volume, indicating miscalculations or incorrect application of the formula. Option D (75.36) is also incorrect, as it does not appropriately reflect the cubic growth of the volume with respect to the radius, resulting in an underestimation.
To find the volume of a sphere, the formula \( V = \frac{4}{3} \pi r^3 \) is used, where \( r \) is the radius. For a radius of 6 cm, the calculation is: \[ V = \frac{4}{3} \pi (6)^3 = \frac{4}{3} \pi (216) \approx 904.32 \, \text{cm}^3 \] Option A (904.32) correctly represents this volume. Option B (150.72) and Option C (25.12) are significantly lower than the actual volume, indicating miscalculations or incorrect application of the formula. Option D (75.36) is also incorrect, as it does not appropriately reflect the cubic growth of the volume with respect to the radius, resulting in an underestimation.
Solve the equation for x: ½ x + 9 = -2/3 x
- A. x=-9/7
- B. x=-54/7
- C. x=-6
- D. x=-54
Correct Answer & Rationale
Correct Answer: B
To solve the equation \( \frac{1}{2}x + 9 = -\frac{2}{3}x \), start by eliminating the fractions. Multiply the entire equation by 6 (the least common multiple of 2 and 3) to obtain \( 3x + 54 = -4x \). Next, combine like terms: adding \( 4x \) to both sides gives \( 7x + 54 = 0 \), leading to \( 7x = -54 \) and thus \( x = -\frac{54}{7} \). Option A is incorrect as it simplifies to a different value. Option C, \( x = -6 \), does not satisfy the original equation. Option D, \( x = -54 \), is also incorrect as it does not balance the equation. Therefore, the only viable solution is \( x = -\frac{54}{7} \).
To solve the equation \( \frac{1}{2}x + 9 = -\frac{2}{3}x \), start by eliminating the fractions. Multiply the entire equation by 6 (the least common multiple of 2 and 3) to obtain \( 3x + 54 = -4x \). Next, combine like terms: adding \( 4x \) to both sides gives \( 7x + 54 = 0 \), leading to \( 7x = -54 \) and thus \( x = -\frac{54}{7} \). Option A is incorrect as it simplifies to a different value. Option C, \( x = -6 \), does not satisfy the original equation. Option D, \( x = -54 \), is also incorrect as it does not balance the equation. Therefore, the only viable solution is \( x = -\frac{54}{7} \).
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.
The graph of the equation y = x^2 + 4x - 5 is shown on the grid. Which statement is true when y = 0?
- A. x= -5 and x=1
- B. x= -2
- C. x= -5 and x = 0
- D. x= -9
Correct Answer & Rationale
Correct Answer: A
To find the values of x when y = 0, we need to solve the equation \(x^2 + 4x - 5 = 0\). Factoring this quadratic gives \((x + 5)(x - 1) = 0\), leading to the solutions \(x = -5\) and \(x = 1\). Option A correctly identifies these solutions. Option B states \(x = -2\), which is not a solution to the equation. Option C suggests \(x = -5\) and \(x = 0\); while it includes one correct solution, \(x = 0\) is incorrect. Option D claims \(x = -9\), which does not satisfy the equation. Thus, only option A accurately reflects the solutions when y = 0.
To find the values of x when y = 0, we need to solve the equation \(x^2 + 4x - 5 = 0\). Factoring this quadratic gives \((x + 5)(x - 1) = 0\), leading to the solutions \(x = -5\) and \(x = 1\). Option A correctly identifies these solutions. Option B states \(x = -2\), which is not a solution to the equation. Option C suggests \(x = -5\) and \(x = 0\); while it includes one correct solution, \(x = 0\) is incorrect. Option D claims \(x = -9\), which does not satisfy the equation. Thus, only option A accurately reflects the solutions when y = 0.