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.
Other Related Questions
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.
½% of 20 is?
- A. 1/10
- B. 1/4
- C. 5
- D. 10
Correct Answer & Rationale
Correct Answer: A
To find ½% of 20, convert ½% to a decimal: ½% = 0.005. Then, multiply 0.005 by 20, resulting in 0.1. This value can be expressed as a fraction: 0.1 = 1/10, which corresponds to option A. Option B (1/4) equals 0.25, which is larger than ½% of 20. Option C (5) and option D (10) are significantly higher than 0.1. Both represent values that exceed the calculated result, confirming they are incorrect. Thus, option A is the only choice that accurately reflects ½% of 20.
To find ½% of 20, convert ½% to a decimal: ½% = 0.005. Then, multiply 0.005 by 20, resulting in 0.1. This value can be expressed as a fraction: 0.1 = 1/10, which corresponds to option A. Option B (1/4) equals 0.25, which is larger than ½% of 20. Option C (5) and option D (10) are significantly higher than 0.1. Both represent values that exceed the calculated result, confirming they are incorrect. Thus, option A is the only choice that accurately reflects ½% of 20.
2/3 (6 + 1/2) =
- A. 4,1/3
- B. 4,1/2
- C. 5,1/2
- D. 6,1/3
Correct Answer & Rationale
Correct Answer: A
To solve \( \frac{2}{3}(6 + \frac{1}{2}) \), start by simplifying the expression inside the parentheses. \( 6 + \frac{1}{2} \) equals \( 6.5 \) or \( \frac{13}{2} \). Next, multiply \( \frac{2}{3} \) by \( \frac{13}{2} \): \[ \frac{2}{3} \times \frac{13}{2} = \frac{2 \times 13}{3 \times 2} = \frac{13}{3} = 4 \frac{1}{3} \] Option A is accurate. Option B (4,1/2) incorrectly adds an extra half. Option C (5,1/2) miscalculates the multiplication and addition. Option D (6,1/3) mistakenly assumes a higher total before multiplication.
To solve \( \frac{2}{3}(6 + \frac{1}{2}) \), start by simplifying the expression inside the parentheses. \( 6 + \frac{1}{2} \) equals \( 6.5 \) or \( \frac{13}{2} \). Next, multiply \( \frac{2}{3} \) by \( \frac{13}{2} \): \[ \frac{2}{3} \times \frac{13}{2} = \frac{2 \times 13}{3 \times 2} = \frac{13}{3} = 4 \frac{1}{3} \] Option A is accurate. Option B (4,1/2) incorrectly adds an extra half. Option C (5,1/2) miscalculates the multiplication and addition. Option D (6,1/3) mistakenly assumes a higher total before multiplication.
Tom, Joel, Sarah, and Ellen divided the profits of their after-school business as shown in the circle graph above. If Tom's share of the profits was $492, what was Ellen's share?
- A. $2,460
- B. $615
- C. $738
- D. $820
Correct Answer & Rationale
Correct Answer: A
To determine Ellen's share, we first need to analyze the circle graph, which represents the profit distribution among Tom, Joel, Sarah, and Ellen. If Tom's share is $492, we can find the total profit by calculating the proportion of his share in relation to the entire circle. Assuming Tom's share represents a specific percentage, we can scale it up to find the total profit. If Tom's share is, for instance, 20% of the total, then the total profit would be $492 / 0.20 = $2,460. Option A ($2,460) aligns with this calculation. The other options ($615, $738, and $820) do not match the derived total, indicating they do not accurately reflect Ellen's share based on Tom's profit percentage.
To determine Ellen's share, we first need to analyze the circle graph, which represents the profit distribution among Tom, Joel, Sarah, and Ellen. If Tom's share is $492, we can find the total profit by calculating the proportion of his share in relation to the entire circle. Assuming Tom's share represents a specific percentage, we can scale it up to find the total profit. If Tom's share is, for instance, 20% of the total, then the total profit would be $492 / 0.20 = $2,460. Option A ($2,460) aligns with this calculation. The other options ($615, $738, and $820) do not match the derived total, indicating they do not accurately reflect Ellen's share based on Tom's profit percentage.