Question

markus scored 86, 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 sum of first 4 tests

$85 + 92 + 82 + 94 = 353$

Step2: Define average of 5 tests

Let $\mu$ = average of 5 tests. Then $\mu = \frac{353 + x}{5}$

Step3: Relate x to the average

Given $x = \mu - 5$, rearrange to $\mu = x + 5$

Step4: Set equations equal

Substitute $\mu$: $x + 5 = \frac{353 + x}{5}$

Step5: Eliminate denominator

Multiply both sides by 5: $5(x + 5) = 353 + x$

Answer:

5(x + 5) = 353 + x