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Solve for x: x/250 = 3/500
- A. 1.5
- B. 25.5
- C. 1500
- D. 2.5
Correct Answer: A
Rationale: To solve for x in the equation x/250 = 3/500, cross multiply to get x = (250 * 3) / 500. First, calculate the numerator, which is 750. Then, divide 750 by 500 to find x. Therefore, x = 1.5. Thus, the correct answer is A: 1.5.
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Ratio and proportion 0.1:10::x:400 =
- A. 25
- B. 5
- C. 50
- D. 4
Correct Answer: D
Rationale: To solve this proportion, we can set it up as 0.1/10 = x/400. Cross multiply to get x = (0.1 * 400)/10 = 4. Therefore, x equals 4, making choice D the correct answer. When solving proportions, it's crucial to maintain the same relationship between the numbers on both sides of the proportion. In this case, the ratio of 0.1 to 10 should be equal to the ratio of x to 400. By cross multiplying and simplifying, we find that x is 4, confirming choice D as the correct answer.
Ratio and Proportion: 0.3:2 = 15:X (Enter numeric value only.)
- A. 50
- B. 75
- C. 100
- D. 125
Correct Answer: C
Rationale: To find the value of X, first, we need to set up a proportion using the given equation: 0.3/2 = 15/X. Cross multiply to solve for X: 0.3X = 2 * 15. Simplify to get 0.3X = 30. Divide by 0.3 to solve for X: X = 30 / 0.3 = 100. Therefore, the correct answer is C. Choice A (50), B (75), and D (125) are incorrect as they do not satisfy the proportion equation given. A summary of the incorrect choices: A is too low, B is also too low, and D is too high compared to the correct answer of 100.
Subtract: 15.7 - 9.8 =
- A. 6.1
- B. 8.96
- C. 5.9
- D. 4.3
Correct Answer: C
Rationale: To subtract two decimal numbers, align the decimal points and then subtract each place value. In this case, 15.7 - 9.8 = 5.9. Therefore, the correct answer is 5.9. When subtracting decimals, it is crucial to maintain the alignment of the decimal points to ensure accurate calculations. In this subtraction problem, the tenths and ones places are being subtracted individually. Subtracting 8 from 7 in the tenths place results in 1, while subtracting 9 from 15 in the ones place results in 6. Combining these results, we get a final answer of 5.9.
What is the result of adding 2/3 and 4/9?
- A. 1 (1/9)
- B. 1 (1/3)
- C. 2/9
- D. 10/9
Correct Answer: A
Rationale: To add 2/3 and 4/9, you need to find a common denominator. In this case, the common denominator is 9. Convert 2/3 to 6/9. Now, the addition becomes 6/9 + 4/9 = 10/9. Simplifying 10/9 gives you 1 (1/9). Therefore, the correct answer is 1 (1/9). When adding fractions, having a common denominator is essential for accurate calculation.
After the expiration date, a vitamin's calcium content decreases. If each tablet initially contains 500 mg of calcium, and 325 mg deteriorates, what is the remaining total amount of calcium per tablet?
- A. 175 mg
- B. 185 mg
- C. 135 mg
- D. 200 mg
Correct Answer: A
Rationale: To determine the remaining calcium content per tablet, subtract the deteriorated amount from the initial amount: 500 mg - 325 mg = 175 mg. After deterioration, each tablet will have 175 mg of calcium remaining. Therefore, the correct answer is A (175 mg). The calculation involves simple subtraction to find the difference between the initial calcium content and the deteriorated amount, providing the accurate remaining total calcium content per tablet.