Solve the problem.
-The amount of a pain reliever that a physician prescribes for a child varies directly as the weight of the child. A physician prescribes $170 \mathrm { mg }$ of the medicine for a 20-lb child.
a. How much medicine would be prescribed for a 40-b child?
b. If $140 \mathrm { mg }$ of medicine was prescribed, what is the weight of the child?
A) a. $340 \mathrm { mg }$
b. $- 5 \mathrm { lb }$
B) a. $190 \mathrm { mg }$
b. $- 5 \mathrm { lb }$
C) a. $190 \mathrm { mg }$
b. $16.47 \mathrm { lb }$
D) a. $340 \mathrm { mg }$
b. $16.47 \mathrm { lb }$

Question

Quizplus · Accepted Answer

The amount of medicine prescribed varies directly with the weight of the child, so we use the formula $ \frac{170 \, \text{mg}}{20 \, \text{lb}} = \frac{x \, \text{mg}}{40 \, \text{lb}} $ for part a, solving for $x$ gives $340 \, \text{mg}$. For part b, using the direct variation formula $ \frac{140 \, \text{mg}}{x \, \text{lb}} = \frac{170 \, \text{mg}}{20 \, \text{lb}} $, solving for $x$ gives $16.47 \, \text{lb}$.

Solve the Problem 170mg170 \mathrm { mg }170mg Of the Medicine for a 20-Lb Child

Solve the Problem $170 \mathrm { mg }$ Of the Medicine for a 20-Lb Child