Question

1. rachels chemistry class has 4 unit exams and a final. she needs at least an average of 85 (a letter grade of b) in order to keep her scholarship. if her unit exam scores are 75, 89, 79 and 92, what is the grade rachel needs on her final exam in order to keep her scholarship? step 1: identify the unknown step 2: write an equation. step 3: solve the equation found in step 2. step 4: answer the question given in the problem

Explanation:

Step1: Identify the unknown

Let \( x \) be the grade Rachel needs on her final exam.

Step2: Write an equation

The average of her 4 unit exams and 1 final exam should be at least 85. The formula for the average is the sum of all scores divided by the number of scores. So we have:

$$ \frac{75 + 89 + 79 + 92 + x}{5} \geq 85 $$

Step3: Solve the equation

First, calculate the sum of her unit exam scores: \( 75 + 89 + 79 + 92 = 335 \).
Substitute this into the equation:

$$ \frac{335 + x}{5} \geq 85 $$

Multiply both sides by 5:

$$ 335 + x \geq 425 $$

Subtract 335 from both sides:

$$ x \geq 425 - 335 $$

$$ x \geq 90 $$

Step4: Answer the question

Rachel needs at least a 90 on her final exam to keep her scholarship.

Answer:

Rachel needs at least a 90 on her final exam.