Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A nutritionist is analyzing the nutritional content of a meal. The amount of protein P (in grams) in the meal is related to the amount of carbohydrates C (in grams) by the equation 3P + 2C = 120. If a meal contains 24 grams of carbohydrates, how many grams of protein does it contain?
- A16 grams
- B36 grams
- C24 grams
- D48 grams
Show answer & explanationAnswer & explanation
Correct answer: C. 24 grams
Substitute C = 24 into the equation 3P + 2C = 120. This gives 3P + 2(24) = 120. Simplify to 3P + 48 = 120. Subtract 48 from both sides: 3P = 72. Divide by 3: P = 24.
Why the other options are wrong
- A. Incorrect. This would be 48/3, if 2C was 48 and you incorrectly divided 48 by 3 for P.
- B. Incorrect. This might be 108/3 if C was 6, or a calculation error.
- D. Incorrect. This is the amount of carbohydrates given, not protein.
Solving Linear Equations with One Variable
The process of finding the value of an unknown variable that satisfies a linear equation by isolating the variable using inverse operations.
- Goal: Isolate the variable.
- Use inverse operations (add/subtract, multiply/divide).
- Maintain balance: do the same operation to both sides.
Memory trick: Balance the scales! Whatever you do to one side, do to the other.