a. To find the daily dose for a man who weighs 175 pounds, we can set up a proportion. Since the rate is 275 mg for every 50 pounds, we can write it as:
275 mg / 50 pounds = x mg / 175 pounds
Cross-multiplying, we get:
275 * 175 = 50 * x
Simplifying, we find:
x = (275 * 175) / 50
So, the daily dose for a man who weighs 175 pounds would be x mg.
b. To determine if the man is receiving the proper dosage, we need to calculate the amount of medicine he would receive in 24 hours. If he is receiving 500 mg every 8 hours, we can multiply that by 3 to get the amount in 24 hours:
500 mg * 3 = 1500 mg
If the daily dose for a man who weighs 175 pounds (as calculated in part a) is greater than or equal to 1500 mg, then he is receiving the proper dosage.