GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A nutritionist is creating a meal plan. They want the total calories (C) from two types of food, Food A and Food B, to be exactly 1500. Food A has 200 calories per serving and Food B has 150 calories per serving. If 'a' represents the number of servings of Food A and 'b' represents the number of servings of Food B, which equation represents this situation?
- A200a + 150b = 1500
- B350(a + b) = 1500
- C150a + 200b = 1500
- Da + b = 1500
Show answer & explanationAnswer & explanation
Correct answer: A. 200a + 150b = 1500
The total calories from Food A is 200 calories/serving * 'a' servings, or 200a. The total calories from Food B is 150 calories/serving * 'b' servings, or 150b. The sum of these two amounts must equal the total desired calories, 1500. Therefore, the equation is 200a + 150b = 1500.
Why the other options are wrong
- B. This equation incorrectly assumes that the total calories per serving (200 + 150 = 350) is multiplied by the sum of servings, implying both foods have the same calorie content.
- C. This equation incorrectly assigns the calorie values to the wrong food types.
- D. This equation incorrectly assumes that the number of servings directly sums to 1500 calories, ignoring the calorie content per serving.
Translating Word Problems to Linear Equations
Converting a real-world scenario described in words into a mathematical equation involving variables, constants, and operators to represent relationships.
- Identify unknowns (variables).
- Identify knowns (constants).
- Look for keywords indicating operations (sum, product, 'is', 'equals').
Memory trick: Read, Define, Translate, Check: Turn words into math!