Solve for X

Question

4 : 5 = x : 10
4 : 8 = x : 16
The physician ordered acetaminophen tabs, 650 mg. Available are acetaminophen tabs, 325 mg. How many tablets will you give? _________

Answer 1

To solve for \( x \) in the ratios:

1. For the first ratio \( 4 : 5 = x : 10 \): \[ \frac{4}{5} = \frac{x}{10} \] Cross-multiply: \[ 4 \times 10 = 5 \times x \implies 40 = 5x \] Solve for \( x \): \[ x = \frac{40}{5} = 8 \]

2. For the second ratio \( 4 : 8 = x : 16 \): \[ \frac{4}{8} = \frac{x}{16} \] Simplify \( \frac{4}{8} = \frac{1}{2} \): \[ \frac{1}{2} = \frac{x}{16} \] Cross-multiply: \[ 1 \times 16 = 2 \times x \implies 16 = 2x \] Solve for \( x \): \[ x = \frac{16}{2} = 8 \]

Now, for the acetaminophen dosage:

• The physician ordered 650 mg.
• The available tablets are 325 mg each.

To find out how many tablets are needed: \[ \text{Number of tablets} = \frac{\text{Ordered dosage}}{\text{Available dosage per tablet}} = \frac{650 , \text{mg}}{325 , \text{mg/tablet}} = 2 \]

So, you will give 2 tablets of acetaminophen.