GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A production manager is tracking the output of two machines. Machine A produces 50 units per hour plus an initial setup batch of 20 units. Machine B produces 60 units per hour with no initial setup batch. After how many hours will Machine B have produced the same number of units as Machine A?
- A3 hours
- B1 hour
- C4 hours
- D2 hours
Show answer & explanationAnswer & explanation
Correct answer: D. 2 hours
To solve this, set up equations for each machine's production and find when they are equal. Machine A: A = 50h + 20. Machine B: B = 60h. Set 50h + 20 = 60h and solve for h.
Why the other options are wrong
- A. Incorrect. At 3 hours, Machine A has 170 units and Machine B has 180 units.
- B. Incorrect. At 1 hour, Machine A has 70 units and Machine B has 60 units.
- C. Incorrect. At 4 hours, Machine A has 220 units and Machine B has 240 units.
Solving Linear Equations
Finding the value(s) of the variable(s) that make a linear equation true. This often involves isolating the variable on one side of the equation.
- Linear equations have variables raised to the power of 1.
- Operations (addition, subtraction, multiplication, division) must be applied equally to both sides.
- The goal is to isolate the variable.
Memory trick: Balance the scale to hit the target variable.