ACT (Enhanced)MathematicsMedium
A scientist is conducting an experiment where the temperature (T) in degrees Celsius at a certain depth (d) in meters is given by the linear equation T = 15 - 0.2d. At what depth, in meters, will the temperature be 5 degrees Celsius?
- A50 meters
- B30 meters
- C25 meters
- D75 meters
Show answer & explanationAnswer & explanation
Correct answer: A. 50 meters
Substitute T = 5 into the equation: 5 = 15 - 0.2d. Subtract 15 from both sides: 5 - 15 = -0.2d, which simplifies to -10 = -0.2d. Divide by -0.2: d = -10 / -0.2 = 50 meters.
Why the other options are wrong
- B. This would result if 0.2d = 9 (15-9=6 not 5).
- C. This would result if the temperature was 10 degrees (15 - 0.2d = 10 => 0.2d = 5 => d = 25).
- D. This would result if 0.2d = 10 and then division error (10/0.2 = 50 not 75).
Solving Linear Equations
Solving a linear equation involves isolating the unknown variable using inverse operations (addition/subtraction, multiplication/division) while maintaining equality.
- The goal is to get the variable by itself on one side of the equation.
- Perform the same operation on both sides of the equation.
- Often involves multiple steps following order of operations in reverse.
Memory trick: Balance the scale! Do unto one side as you do unto the other.