Question

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alicias test scores are 77, 86, 66, and 80. what score does she need on the last test in order to average 80 on her tests?

Explanation:

Step1: Recall the average formula

The average of a set of numbers is the sum of the numbers divided by the count of the numbers. Let the score on the last test be \( x \). There are a total of \( 4 + 1=5 \) tests. The average is 80, so we can set up the equation: \(\frac{77 + 86 + 66 + 80 + x}{5}=80\)

Step2: Simplify the numerator

First, calculate the sum of the known scores: \( 77+86 + 66+80=309 \). So the equation becomes \(\frac{309 + x}{5}=80\)

Step3: Solve for \( x \)

Multiply both sides of the equation by 5: \( 309+x = 80\times5\). Calculate \( 80\times5 = 400 \), so \( 309+x=400 \). Then subtract 309 from both sides: \( x=400 - 309 \)

Step4: Calculate the value of \( x \)

\( 400-309 = 91 \)

Answer:

91