Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A veterinarian is calculating medication dosages. A dog weighs 45 pounds. If the recommended dosage is 25 milligrams of medication per 5 pounds of body weight, how many milligrams of medication should the dog receive?
- A125 mg
- B250 mg
- C180 mg
- D225 mg
Show answer & explanationAnswer & explanation
Correct answer: D. 225 mg
First, find the unit dosage: 25 mg / 5 lbs = 5 mg per pound. Then, multiply the unit dosage by the dog's weight: 5 mg/lb * 45 lbs = 225 mg. Alternatively, set up a proportion: 25 mg / 5 lbs = x mg / 45 lbs. Cross-multiply: 25 * 45 = 5 * x. 1125 = 5x. x = 225.
Why the other options are wrong
- A. This would be the result if the dog weighed 25 pounds.
- B. This would be the result if the dog weighed 50 pounds.
- C. This would be the result if the dosage was 4 mg per pound.
Proportional Reasoning
Proportional reasoning involves understanding how quantities relate to each other in a consistent ratio. It is used to solve problems where one quantity changes in direct relation to another, often by setting up and solving proportions.
- A proportion is an equality between two ratios.
- Cross-multiplication is a common method to solve for an unknown in a proportion.
- Unit rates are a specific form of proportional reasoning.
Memory trick: Ratio up, cross-multiply down, solve around.