GMAT Focus EditionQuantitative ReasoningMedium
A factory produces widgets at a constant rate. Machine A produces 'x' widgets per hour, and Machine B produces 'y' widgets per hour. If Machine A works for 3 hours and Machine B works for 5 hours, they produce a total of 750 widgets. If Machine A works for 5 hours and Machine B works for 3 hours, they produce a total of 850 widgets. What is the production rate of Machine A (widgets per hour)?
- A125
- B150
- C80
- D100
Show answer & explanationAnswer & explanation
Correct answer: A. 125
Let x be the rate of Machine A and y be the rate of Machine B. The given information translates to two equations: 3x + 5y = 750 and 5x + 3y = 850. Multiplying the first equation by 3 and the second by 5 gives 9x + 15y = 2250 and 25x + 15y = 4250. Subtracting the first from the second yields 16x = 2000, so x = 125. Substituting x=125 into the first equation: 3(125) + 5y = 750 => 375 + 5y = 750 => 5y = 375 => y = 75.
Why the other options are wrong
- B. This is incorrect; it might be a result of algebraic error or miscalculation.
- C. This is incorrect; it might be the rate of Machine B or a result of algebraic error.
- D. This is incorrect; it might be a result of algebraic error or miscalculation.
System of Linear Equations (Word Problems)
Solving real-world problems by translating them into two or more linear equations and finding the values of the variables that satisfy all equations simultaneously.
- Define variables for unknown quantities.
- Formulate equations based on the problem's conditions.
- Use substitution or elimination methods to solve the system.
- Often involves rates, quantities, costs, or mixtures.
Memory trick: Read, define, equation-ize, then solve and verify the prize.