Isabel earns $15.80 per hour for the first 8 hours she works each day. She earns 1.5 times her hourly rate for all time after the first 8 hours. How much does Isabel earn on a day when she works 8.5 hours?
- A. 126.4
- B. 138.25
- C. 189.6
- D. 201.45
- E. 237
Correct Answer & Rationale
Correct Answer: B
To determine Isabel's earnings for an 8.5-hour workday, first calculate her earnings for the first 8 hours at $15.80 per hour, which totals $126.40 (8 hours × $15.80/hour). For the additional 0.5 hours, she earns 1.5 times her hourly rate, which is $23.70 (1.5 × $15.80). Therefore, for the extra half hour, she earns $11.85 (0.5 hours × $23.70/hour). Adding these amounts together gives $138.25 ($126.40 + $11.85). Option A ($126.40) only accounts for the first 8 hours. Option C ($189.60) incorrectly assumes full-time pay without considering the overtime rate. Option D ($201.45) miscalculates the overtime pay, while Option E ($237) overestimates by not applying the correct hourly rates.
To determine Isabel's earnings for an 8.5-hour workday, first calculate her earnings for the first 8 hours at $15.80 per hour, which totals $126.40 (8 hours × $15.80/hour). For the additional 0.5 hours, she earns 1.5 times her hourly rate, which is $23.70 (1.5 × $15.80). Therefore, for the extra half hour, she earns $11.85 (0.5 hours × $23.70/hour). Adding these amounts together gives $138.25 ($126.40 + $11.85). Option A ($126.40) only accounts for the first 8 hours. Option C ($189.60) incorrectly assumes full-time pay without considering the overtime rate. Option D ($201.45) miscalculates the overtime pay, while Option E ($237) overestimates by not applying the correct hourly rates.
Other Related Questions
The relationship between h, a person's height in inches, and f, the length in inches of the person's femur, is modeled by the equation: h = 1.88f + 32. Which statement correctly identifies and describes the slope of the equation?
- A. The slope of the equation is 1.88, and it represents the femur length, in inches, when the height is 32 inches.
- B. The slope of the equation is 1.88, and it represents the number of inches the height increases for each inch the femur length increases
- C. The slope of the equation is 1.88, and it represents the number of inches the femur length increases for each inch the height increases
- D. The slope of the equation is 32, and it represents the number of inches the height increases for each inch the femur length increases.
- E. The slope of the equation is 32, and it represents the height, in inches, when the femur length is 1.88 inches.
Correct Answer & Rationale
Correct Answer: B
The slope of 1.88 in the equation h = 1.88f + 32 indicates that for every additional inch in femur length (f), height (h) increases by 1.88 inches. This relationship highlights the direct impact of femur length on height. Option A misinterprets the slope, incorrectly stating it represents femur length at a specific height. Option C reverses the relationship, suggesting femur length increases with height, which is inaccurate. Option D incorrectly identifies the slope as 32 and misrepresents the relationship. Option E also incorrectly identifies the slope and misinterprets its meaning in the context of the equation.
The slope of 1.88 in the equation h = 1.88f + 32 indicates that for every additional inch in femur length (f), height (h) increases by 1.88 inches. This relationship highlights the direct impact of femur length on height. Option A misinterprets the slope, incorrectly stating it represents femur length at a specific height. Option C reverses the relationship, suggesting femur length increases with height, which is inaccurate. Option D incorrectly identifies the slope as 32 and misrepresents the relationship. Option E also incorrectly identifies the slope and misinterprets its meaning in the context of the equation.
How many solutions does the equation 3x + 9 = 3x - 12 have?
- B. 1
- C. 2
- D. 3
- E. Infinitely many
Correct Answer & Rationale
Correct Answer: A
To determine the number of solutions for the equation 3x + 9 = 3x - 12, we can simplify both sides. Subtracting 3x from each side results in 9 = -12, which is a false statement. Since the equation leads to a contradiction, it indicates that there are no values of x that can satisfy it. Option B (1 solution) suggests a single value exists, which is incorrect. Option C (2 solutions) and D (3 solutions) imply multiple valid values, which is also false. Option E (infinitely many solutions) suggests that any x would satisfy the equation, which is not true given the contradiction. Thus, the equation has no solutions.
To determine the number of solutions for the equation 3x + 9 = 3x - 12, we can simplify both sides. Subtracting 3x from each side results in 9 = -12, which is a false statement. Since the equation leads to a contradiction, it indicates that there are no values of x that can satisfy it. Option B (1 solution) suggests a single value exists, which is incorrect. Option C (2 solutions) and D (3 solutions) imply multiple valid values, which is also false. Option E (infinitely many solutions) suggests that any x would satisfy the equation, which is not true given the contradiction. Thus, the equation has no solutions.
Connor sprinted 55 yards in 6.25 seconds. What was Connor's average speed in miles per hour?
- A. 6
- B. 9
- C. 15
- D. 18
- E. 26
Correct Answer & Rationale
Correct Answer: D
To find Connor's average speed in miles per hour, we first convert 55 yards to miles. There are 1,760 yards in a mile, so 55 yards is approximately 0.0312 miles. Next, we convert 6.25 seconds to hours by dividing by 3,600 (the number of seconds in an hour), resulting in about 0.001736 hours. Average speed is calculated by dividing distance by time: 0.0312 miles / 0.001736 hours ≈ 18 mph. Option A (6 mph) and B (9 mph) underestimate Connor's speed, while C (15 mph) is also too low. E (26 mph) overestimates it. Thus, 18 mph is the accurate average speed.
To find Connor's average speed in miles per hour, we first convert 55 yards to miles. There are 1,760 yards in a mile, so 55 yards is approximately 0.0312 miles. Next, we convert 6.25 seconds to hours by dividing by 3,600 (the number of seconds in an hour), resulting in about 0.001736 hours. Average speed is calculated by dividing distance by time: 0.0312 miles / 0.001736 hours ≈ 18 mph. Option A (6 mph) and B (9 mph) underestimate Connor's speed, while C (15 mph) is also too low. E (26 mph) overestimates it. Thus, 18 mph is the accurate average speed.
The expression 6a + 4c represents the total price, in dollars, of admission to an air show for a adults and c children. On Saturday, 380 adults and 120 children paid admission to the air show. What was the total price of admission for those people?
- A. 524
- B. 2240
- C. 2760
- D. 5000
- E. 12000
Correct Answer & Rationale
Correct Answer: C
To find the total price of admission, substitute the values of adults (a) and children (c) into the expression 6a + 4c. Here, a = 380 and c = 120. Calculating: 6(380) + 4(120) = 2280 + 480 = 2760. Thus, the total price is 2760 dollars. Option A (524) is too low, as it doesn't account for the number of attendees. Option B (2240) underestimates the total, likely misunderstanding the pricing structure. Option D (5000) and Option E (12000) are excessively high, suggesting a miscalculation or misunderstanding of the pricing per adult and child.
To find the total price of admission, substitute the values of adults (a) and children (c) into the expression 6a + 4c. Here, a = 380 and c = 120. Calculating: 6(380) + 4(120) = 2280 + 480 = 2760. Thus, the total price is 2760 dollars. Option A (524) is too low, as it doesn't account for the number of attendees. Option B (2240) underestimates the total, likely misunderstanding the pricing structure. Option D (5000) and Option E (12000) are excessively high, suggesting a miscalculation or misunderstanding of the pricing per adult and child.