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

Explanation:

Step1: Calculate the sum of the first four test scores

The sum of the first four test scores is \(85 + 92+82 + 94=353\).

Step2: Express the average of the five - test scores

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

Step3: Set up the equation based on the given relationship

Since the score of the fifth test \(x\) is five points lower than the average of all five tests, we have \(x=\frac{353 + x}{5}-5\).
Multiply both sides of the equation by \(5\) to get \(5x=353 + x-25\), which simplifies to \(5(x + 5)=353 + x\).

Answer:

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