The fraction x/24 is equal to 0.75. What is the value of x?
- A. 3
- B. 6
- C. 9
- D. 18
Correct Answer & Rationale
Correct Answer: D
To find the value of x in the equation x/24 = 0.75, we start by converting 0.75 to a fraction, which is 75/100 or 3/4. Setting the two fractions equal gives us x/24 = 3/4. Cross-multiplying leads to 4x = 72. Dividing both sides by 4 results in x = 18. Option A (3) is too low; substituting it back yields 3/24 = 0.125. Option B (6) also falls short, as 6/24 = 0.25. Option C (9) gives 9/24 = 0.375, still incorrect. Only option D (18) satisfies the original equation, confirming its validity.
To find the value of x in the equation x/24 = 0.75, we start by converting 0.75 to a fraction, which is 75/100 or 3/4. Setting the two fractions equal gives us x/24 = 3/4. Cross-multiplying leads to 4x = 72. Dividing both sides by 4 results in x = 18. Option A (3) is too low; substituting it back yields 3/24 = 0.125. Option B (6) also falls short, as 6/24 = 0.25. Option C (9) gives 9/24 = 0.375, still incorrect. Only option D (18) satisfies the original equation, confirming its validity.
Other Related Questions
3/8 expressed as a percent is
- A. 3.75%
- B. 37.50%
- C. 38%
- D. 38,1/3%
Correct Answer & Rationale
Correct Answer: B
To convert a fraction to a percent, multiply by 100. For 3/8, the calculation is (3 ÷ 8) × 100, which equals 37.5%. This aligns with option B: 37.50%. Option A (3.75%) results from miscalculating the fraction, likely confusing the decimal representation. Option C (38%) rounds up incorrectly, as it does not accurately reflect the precise conversion. Option D (38, 1/3%) misrepresents the fraction by suggesting a value that exceeds the actual percentage, further indicating a misunderstanding of the conversion process. Thus, option B is the only accurate representation of 3/8 as a percent.
To convert a fraction to a percent, multiply by 100. For 3/8, the calculation is (3 ÷ 8) × 100, which equals 37.5%. This aligns with option B: 37.50%. Option A (3.75%) results from miscalculating the fraction, likely confusing the decimal representation. Option C (38%) rounds up incorrectly, as it does not accurately reflect the precise conversion. Option D (38, 1/3%) misrepresents the fraction by suggesting a value that exceeds the actual percentage, further indicating a misunderstanding of the conversion process. Thus, option B is the only accurate representation of 3/8 as a percent.
Alexia, Bob, and Comelia recorded the number of pages of books they read last month. Alexia read 135 pages, Bob read 26 pages less than Alexia, and Comelia read 3 and one-half times more pages than Alexia and Bob combined. Which of the following represents the total number of pages that Alexia, Bob, and Comelia read last month?
- A. 3.5(135 + 26)
- B. 3.5[2(135) - 26]
- C. 4.5[2(135) - 26]
- D. 4.5[2(135) + 26]
Correct Answer & Rationale
Correct Answer: C
To determine the total number of pages read, first calculate Bob's pages: he read 135 - 26 = 109 pages. The combined pages of Alexia and Bob is 135 + 109 = 244 pages. Comelia read 3.5 times this total, resulting in 3.5 × 244. Option A incorrectly uses 135 + 26, which does not account for Bob's actual pages read. Option B mistakenly uses a subtraction instead of addition for the combined total. Option D incorrectly adds Bob's pages instead of using the correct combined total for Comelia's calculation. Thus, C accurately represents the total with 3.5(244), leading to the correct final total.
To determine the total number of pages read, first calculate Bob's pages: he read 135 - 26 = 109 pages. The combined pages of Alexia and Bob is 135 + 109 = 244 pages. Comelia read 3.5 times this total, resulting in 3.5 × 244. Option A incorrectly uses 135 + 26, which does not account for Bob's actual pages read. Option B mistakenly uses a subtraction instead of addition for the combined total. Option D incorrectly adds Bob's pages instead of using the correct combined total for Comelia's calculation. Thus, C accurately represents the total with 3.5(244), leading to the correct final total.
Which of the following inequalities is true?
- A. 0.7 < 0.1 < 0.11 < 0.101
- B. 0.1 < 0.7 < 0.101 < 0.11
- C. 0.1 < 0.7 < 0.11 < 0.101
- D. 0.1 < 0.101 < 0.11 < 0.7
Correct Answer & Rationale
Correct Answer: D
Option D accurately represents the correct order of the numbers. When comparing the values, 0.1 is the smallest, followed by 0.101, then 0.11, and finally 0.7, which is the largest. Option A is incorrect as it mistakenly places 0.7 as less than both 0.1 and 0.11, which is not true. Option B incorrectly suggests that 0.101 is less than 0.11, which is also inaccurate. Option C places 0.11 before 0.101, misrepresenting their actual values. Thus, D is the only option that correctly orders the numbers from smallest to largest.
Option D accurately represents the correct order of the numbers. When comparing the values, 0.1 is the smallest, followed by 0.101, then 0.11, and finally 0.7, which is the largest. Option A is incorrect as it mistakenly places 0.7 as less than both 0.1 and 0.11, which is not true. Option B incorrectly suggests that 0.101 is less than 0.11, which is also inaccurate. Option C places 0.11 before 0.101, misrepresenting their actual values. Thus, D is the only option that correctly orders the numbers from smallest to largest.
John worked at a bookstore for two weeks. The second week he earned 20 percent more than he did the first week. If he earned $300 the second week, how much did he earn the first week?
- A. 240
- B. 250
- C. 280
- D. 380
Correct Answer & Rationale
Correct Answer: B
To determine John’s earnings for the first week, we know that his second week earnings were 20% more than the first week. If he earned $300 in the second week, we can calculate his first week earnings by setting up the equation: Let x be the first week’s earnings. Then, x + 0.2x = 300. This simplifies to 1.2x = 300. Dividing both sides by 1.2 gives x = 250. Option A ($240) is too low, as it would not result in a $300 second week. Option C ($280) would imply a second week earning of $336, which exceeds $300. Option D ($380) is also incorrect as it suggests a second week earning of $456. Thus, $250 is the only viable answer.
To determine John’s earnings for the first week, we know that his second week earnings were 20% more than the first week. If he earned $300 in the second week, we can calculate his first week earnings by setting up the equation: Let x be the first week’s earnings. Then, x + 0.2x = 300. This simplifies to 1.2x = 300. Dividing both sides by 1.2 gives x = 250. Option A ($240) is too low, as it would not result in a $300 second week. Option C ($280) would imply a second week earning of $336, which exceeds $300. Option D ($380) is also incorrect as it suggests a second week earning of $456. Thus, $250 is the only viable answer.