Q: Suppose Shureka scores 90 on her final exam. What will her average be?

$$\frac{88 + 74 + 83 + 61 + 2 \times 90}{6} = 81$$

Q: If Shureka scores 100 on her final, what is her average?

$$\frac{88 + 74 + 83 + 61 + 2 \times 100}{6} = 84.33$$

Question 1

Shureka Washburn has test scores of 88, 74, 83, and 61. If her final exam counts as two tests, which inequality represents the minimum score $$x$$ she must earn on the final to achieve an average of at least 77?

Accepted Answer

$$\frac{88 + 74 + 83 + 61 + 2x}{6} \geq 77$$

Question 2

After simplifying $$88 + 74 + 83 + 61 + 2x$$, what is the correct expression for the numerator?

Accepted Answer

$$306 + 2x$$

Question 3

What is the next algebraic step after writing $$\frac{306 + 2x}{6} \geq 77 to $$solve for $$x$$?

Accepted Answer

Multiply both sides by 6

Question 4

What is the result after multiplying both sides of $$\frac{306 + 2x}{6} \geq 77 by 6$$?

Accepted Answer

$$306 + 2x \geq 462$$

Question 5

After simplifying $$306 + 2x \geq 462$$, what is the next step to isolate $$x$$?

Accepted Answer

Subtract 306 from both sides

Question 6

What is the solution to $$2x \geq 156$$?

Accepted Answer

$$x \geq 78$$

Question 7

If Shureka scores exactly 78 on her final exam, what will her average be?

Accepted Answer

77

Question 8

Which of the following best explains the meaning of the solution $$x \geq 78 in $$the context of the problem?

Accepted Answer

She must score at least 78 on the final to pass with an average of 77 or higher.

Question 9

If the final exam only counted as one test, what would the inequality for the minimum score $$x be to $$achieve an average of 77?

Accepted Answer

$$\frac{88 + 74 + 83 + 61 + x}{5} \geq 77$$

Question 10

Suppose Shureka scores 90 on her final exam. What will her average be?

Accepted Answer

$$\frac{88 + 74 + 83 + 61 + 2 	imes 90}{6} = 81$$

Question 11

Which of the following is a correct interpretation of the average formula used in this scenario?

Accepted Answer

The average is the total score divided by the total number of test counts, including the final as two tests.

Question 12

If Shureka wants an average of at least 80, what is the minimum score she must earn on the final exam?

Accepted Answer

$$x \geq 82$$

Question 13

Which step is necessary to clear the denominator in the inequality $$\frac{306 + 2x}{6} \geq 77$$?

Accepted Answer

Multiply both sides by 6

Question 14

If Shureka scores 100 on her final, what is her average?

Accepted Answer

$$\frac{88 + 74 + 83 + 61 + 2 	imes 100}{6} = 84.33$$

Finding the Minimum Final Exam Score Needed for a Desired Average

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