Question

markus scored 85, 92, 82, and 94 on the first four tests of the semester. his teacher has not yet told him his score on his fifth test, but did tell him that his score on the fifth test is five points lower than the average (arithmetic mean) of all five tests. which equation could markus use to determine the score of the fifth test, x? 4(x + 5) = 353 + x; 5(x + 5) = 353 + x; 5(x - 5) = 353 + x; 4(x - 5) = 353 + x

Explanation:

Step1: Calculate sum of first four tests

Sum of 85, 92, 82, 94: \(85 + 92 + 82 + 94 = 353\).

Step2: Define average of five tests

Let fifth test score be \(x\). Average of five tests is \(\frac{353 + x}{5}\).

Step3: Relate fifth test score to average

Fifth test score \(x\) is 5 less than average: \(x = \frac{353 + x}{5} - 5\).
Multiply both sides by 5: \(5x = 353 + x - 25\), simplify to \(5(x + 5) = 353 + x\) (since \(x + 5=\frac{353 + x}{5}\), multiply by 5 gives \(5(x + 5)=353 + x\)).

Answer:

\(5(x + 5) = 353 + x\) (the middle equation)