1Cademy - Solving a Proportion Application: Medication Dosage by Childs Weight

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Solving a Proportion Application: Medication Dosage by Child's Weight

Apply the proportion-solving strategy to a real-world medical dosage problem.

Problem: Pediatricians prescribe $5$ milliliters (ml) of acetaminophen for every $25$ pounds of a child's weight. If Zoe weighs $80$ pounds, how many milliliters of acetaminophen will her doctor prescribe?

Identify what to find and assign a variable: How many ml of acetaminophen should be prescribed? Let $a$ = ml of acetaminophen.
Translate into a proportion, keeping units consistent on each side — milliliters over pounds equals milliliters over pounds:

$\frac{5}{25} = \frac{a}{80}$

Solve by multiplying both sides by the LCD, which is $400$ :

$400 \cdot \frac{5}{25} = 400 \cdot \frac{a}{80}$

Remove common factors on each side. On the left, $\frac{400}{25} = 16$ , so the left side becomes $16 \cdot 5$ . On the right, $\frac{400}{80} = 5$ , so the right side becomes $5a$ :

$16 \cdot 5 = 5a$

Divide both sides by $5$ :

$16 = a$

Check reasonableness: Since $80$ is approximately $3$ times $25$ , the dosage should be roughly $3$ times $5$ , which is $15$ . The answer of $16$ ml is close and makes sense.
Verify by substituting $a = 16$ back into the original proportion:

$\frac{5}{25} = \frac{16}{80}$

$\frac{1}{5} = \frac{1}{5}$ ✓

Answer: The pediatrician would prescribe $16$ ml of acetaminophen to Zoe.

This example demonstrates a key technique in proportion word problems: aligning the units so that both ratios compare the same quantities in the same order (ml over pounds on both sides). The LCD method then transforms the proportion into a simple linear equation.

Updated 2026-04-30

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