Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A production manager is tracking the output of two different machines. Machine A produces 50 units per hour, and Machine B produces 70 units per hour. If Machine A runs for 'x' hours and Machine B runs for 'y' hours, and their combined output is 460 units, which equation represents this situation?
- A120(x + y) = 460
- B50x + 70y = 460
- C70x + 50y = 460
- Dx + y = 460
Show answer & explanationAnswer & explanation
Correct answer: B. 50x + 70y = 460
The number of units produced by Machine A is its rate (50 units/hour) multiplied by the hours it runs (x), so 50x. Similarly, for Machine B, it's 70y. The combined output is the sum of their individual outputs, so 50x + 70y = 460.
Why the other options are wrong
- A. Incorrect. This equation implies a combined rate of 120 applied to total hours, not individual rates.
- C. Incorrect. This equation swaps the rates for Machine A and Machine B.
- D. Incorrect. This equation would represent the total number of hours worked, not total units.
Translating Word Problems to Linear Equations
The process of converting a real-world scenario described in words into a mathematical linear equation or system of equations to solve for unknown quantities.
- Identify unknown quantities and assign variables.
- Look for keywords indicating operations (sum, product, difference, etc.).
- Formulate equations based on the relationships described.
Memory trick: Read, Define, Translate, Check – like turning a story into math code!