Correct Answer: D

Rationale: To find the value of x, cross multiply in the ratio 18:x=10:300. This gives 18 * 300 = 10 * x. Solving for x, x = 540. Therefore, the correct answer is D. Choice A (16), Choice B (180), and Choice C (30) are incorrect because they do not satisfy the proportion equation 18:x=10:300 when cross multiplied.

Correct Answer: A

Rationale: To find the total tablets in the shipment, first, calculate 1/5 of 6,000: 6,000 * 1/5 = 1,200. Add this to the original order: 6,000 + 1,200 = 7,200 tablets. Therefore, the shipment included 7,200 tablets. Choice B, 5,000 tablets, is incorrect because it does not account for the additional 1/5 of the original order. Choice C, 6,500 tablets, is incorrect as it only considers the original order and not the extra tablets. Choice D, 8,000 tablets, is incorrect as it overestimates the total by not considering the 1/5 more tablets included in the shipment.

Correct Answer: B

Rationale: To calculate the total number of balloons needed, multiply the number of children by the balloons each child will receive: 16 children * 15 balloons = 240 balloons. Since there are 50 balloons per packet, divide the total number of balloons needed by the balloons per packet: 240 balloons · 50 balloons per packet = 4.8 packets. As you cannot buy a fraction of a packet, the mother will need to round up to the nearest whole number of packets, which is 5. Therefore, the correct answer is 5 packets. Choice A (17) is incorrect because it does not accurately calculate the number of packets needed. Choice C (6) is incorrect as it overestimates the number of packets required. Choice D (50) is incorrect as it does not consider the number of children and balloons per child in the calculation.

Correct Answer: A

Rationale: To calculate the dose for a 2-year-old child using Fred's rule, we substitute the child's age (24 months) and the adult dose (15 mg) into the formula: (24 x 15) / 150 = 2.4 mg. Therefore, the correct answer is A, representing 2.4 mg for a 2-year-old child. Choice B is incorrect as it does not match the calculated dose. Choice C is incorrect as it does not consider the formula provided. Choice D is incorrect as it does not reflect the correct calculation based on the given information.

Correct Answer: D

Rationale: To divide mixed numbers, convert them to improper fractions. 5 & 3/4 = 23/4 and 1/2 = 2/1. So, 23/4 · 2/1 = 23/4 * 1/2 = 23/8 = 2 & 7/8. Therefore, 5 & 3/4 divided by 1/2 reduces to 11 & 1/2. Choices A, B, and C are incorrect because they do not represent the correct result of dividing 5 & 3/4 by 1/2.