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
4(x - 5) = 353 + x
5(x - 5) = 353 + x

Explanation:

Step1: Calculate the sum of the first four tests

Sum of first four tests: \(85 + 92+82 + 94=353\)

Step2: Express the average of five tests

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

Step3: Relate \(x\) to the average

Since \(x\) is five points lower than the average, then \(x=\frac{353 + x}{5}-5\)
Multiply both sides by \(5\): \(5x=353 + x-25\), which can be rewritten as \(5(x + 5)=353 + x\)

Answer:

\(5(x + 5)=353 + x\) (the second option)