Question

Acetaminophen is a medicine used to relieve pain and reduce fevers. However, when administering acetaminophen to infants and children, the dosage must be controlled carefully. Otherwise, there could be fatal consequences, such as kidney failure. The dosage usually varies directly as the weight of the child. When a baby weighs 25 pounds, the recommended dosage is 160 mg. Using the previous information, what would the recommended dosage for a child who weighs 75 pounds? (Is this a direct variation problem or an inverse variation problem? What key words in each problem tell you that it is either a direct variation or inverse variable problem?)

Answer 1

The recommended dosage of acetaminophen for a child who weighs 75 pounds is 480 mg by using direct variation and setting up a proportion based on the dosage given to a 25-pound child.

Step-by-step explanation:

The question is about calculating the correct dosage of acetaminophen for a child based on their weight, which is an example of a direct variation problem. Direct variation is indicated by phrases such as 'the dosage usually varies directly as the weight of the child.'

To find the correct dosage for a 75-pound child, we use the fact that a 25-pound baby receives 160 mg. We set up a proportion since the dosage varies directly with weight: 160 mg / 25 pounds = x mg / 75 pounds, where x represents the desired dosage for the 75-pound child.

Solving for x, we get: x = (160 mg / 25 pounds) * 75 pounds = 480 mg. Therefore, the recommended dosage of acetaminophen for a child who weighs 75 pounds is 480 mg.