At the Crest Coffee Shop, the cost of a plain bagel was $0.75 last year. This year the cost of a plain bagel is $0.90. By what percent did the cost of a plain bagel increase from last year to this year?
- A. 10%
- B. 15%
- C. 17%
- D. 20%
Correct Answer & Rationale
Correct Answer: D
To determine the percent increase in the cost of a plain bagel, the formula used is: \[ \text{Percent Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100 \] Substituting the given values: \[ \text{Percent Increase} = \left( \frac{0.90 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.15}{0.75} \right) \times 100 = 20\% \] Option A (10%) underestimates the increase, while B (15%) and C (17%) also fail to reflect the correct calculation. Therefore, the accurate calculation confirms a 20% increase in cost.
To determine the percent increase in the cost of a plain bagel, the formula used is: \[ \text{Percent Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100 \] Substituting the given values: \[ \text{Percent Increase} = \left( \frac{0.90 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.15}{0.75} \right) \times 100 = 20\% \] Option A (10%) underestimates the increase, while B (15%) and C (17%) also fail to reflect the correct calculation. Therefore, the accurate calculation confirms a 20% increase in cost.
Other Related Questions
Linda has borrowed 8 more books than Susan from the school library. Richard has borrowed half as many books as Linda has. If Richard has borrowed 17 books from the library, how many books has Susan borrowed?
- A. 25
- B. 26
- C. 34
- D. 42
Correct Answer & Rationale
Correct Answer: B
To determine how many books Susan has borrowed, start with Richard's 17 books. Since Richard has borrowed half as many books as Linda, Linda must have borrowed 34 books (17 x 2). Given that Linda has borrowed 8 more books than Susan, we can set up the equation: Linda's books = Susan's books + 8. Therefore, if Linda has 34 books, we find Susan's total by subtracting 8: 34 - 8 = 26. Option A (25) is incorrect as it underestimates Susan's total. Option C (34) mistakenly suggests Susan borrowed the same amount as Linda. Option D (42) overestimates Susan's total by not accounting for the difference of 8 books. Thus, the only valid option is 26.
To determine how many books Susan has borrowed, start with Richard's 17 books. Since Richard has borrowed half as many books as Linda, Linda must have borrowed 34 books (17 x 2). Given that Linda has borrowed 8 more books than Susan, we can set up the equation: Linda's books = Susan's books + 8. Therefore, if Linda has 34 books, we find Susan's total by subtracting 8: 34 - 8 = 26. Option A (25) is incorrect as it underestimates Susan's total. Option C (34) mistakenly suggests Susan borrowed the same amount as Linda. Option D (42) overestimates Susan's total by not accounting for the difference of 8 books. Thus, the only valid option is 26.
Harriet took 48 minutes to ride her bike the distance from her house to the town library. If she rode at a constant rate, what fraction of the total distance did she ride in the first 12 minutes?
- A. 1/4
- B. 1/3
- C. 1/2
- D. 3/4
Correct Answer & Rationale
Correct Answer: A
To determine the fraction of the total distance Harriet rode in the first 12 minutes, we start by recognizing that she took 48 minutes for the entire trip. Riding at a constant rate means that her distance covered is proportional to the time spent riding. In 12 minutes, which is one-fourth of the total 48 minutes, she would have covered one-fourth of the total distance. Thus, the fraction of the total distance she rode in the first 12 minutes is 1/4. Options B (1/3), C (1/2), and D (3/4) misrepresent the proportion of time to total time. Each suggests a greater fraction than what corresponds to 12 minutes relative to 48 minutes, leading to incorrect conclusions about the distance covered.
To determine the fraction of the total distance Harriet rode in the first 12 minutes, we start by recognizing that she took 48 minutes for the entire trip. Riding at a constant rate means that her distance covered is proportional to the time spent riding. In 12 minutes, which is one-fourth of the total 48 minutes, she would have covered one-fourth of the total distance. Thus, the fraction of the total distance she rode in the first 12 minutes is 1/4. Options B (1/3), C (1/2), and D (3/4) misrepresent the proportion of time to total time. Each suggests a greater fraction than what corresponds to 12 minutes relative to 48 minutes, leading to incorrect conclusions about the distance covered.
165 is what percent of 150?
- A. 95%
- B. 110%
- C. 111%
- D. 115%
Correct Answer & Rationale
Correct Answer: B
To find what percent 165 is of 150, divide 165 by 150 and then multiply by 100. This calculation yields 110%, indicating that 165 is 110% of 150. Option A (95%) is incorrect as it underestimates the relationship between the two numbers. Option C (111%) slightly overestimates the value, while Option D (115%) significantly exaggerates it. Each of these options fails to accurately represent the proportion of 165 to 150, reinforcing that 110% is the precise measure of this relationship.
To find what percent 165 is of 150, divide 165 by 150 and then multiply by 100. This calculation yields 110%, indicating that 165 is 110% of 150. Option A (95%) is incorrect as it underestimates the relationship between the two numbers. Option C (111%) slightly overestimates the value, while Option D (115%) significantly exaggerates it. Each of these options fails to accurately represent the proportion of 165 to 150, reinforcing that 110% is the precise measure of this relationship.
Of the following, which is closest to (2,12/15 - 1/10) ÷ 16/6 ?
- B. 1
- C. 2
- D. 3
Correct Answer & Rationale
Correct Answer: B
To solve (2, 12/15 - 1/10) ÷ (16/6), first, convert the mixed number 2, 12/15 to an improper fraction: 2 = 30/15, so 2, 12/15 = 30/15 + 12/15 = 42/15. Next, simplify 12/15 - 1/10. Finding a common denominator (30), we have 24/30 - 3/30 = 21/30, which simplifies to 7/10. Thus, we compute (42/15 - 7/10) = (28/10 - 21/30) = (84/30 - 21/30) = 63/30 = 21/10. Dividing by (16/6) equals (21/10) ÷ (8/3) = (21/10) × (3/8) = 63/80, which is closest to 1. Options C and D (2 and 3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result of the division.
To solve (2, 12/15 - 1/10) ÷ (16/6), first, convert the mixed number 2, 12/15 to an improper fraction: 2 = 30/15, so 2, 12/15 = 30/15 + 12/15 = 42/15. Next, simplify 12/15 - 1/10. Finding a common denominator (30), we have 24/30 - 3/30 = 21/30, which simplifies to 7/10. Thus, we compute (42/15 - 7/10) = (28/10 - 21/30) = (84/30 - 21/30) = 63/30 = 21/10. Dividing by (16/6) equals (21/10) ÷ (8/3) = (21/10) × (3/8) = 63/80, which is closest to 1. Options C and D (2 and 3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result of the division.