Math Problem Statement

Melinda's first two test grades in Psychology were 87 and 94. What does she need to make on the third test to maintain an average of at least 90?

Solution

To find out what Melinda needs to score on her third test to maintain an average of at least 90, we can set up the following equation.

Step 1: Set up the equation for the average.

The formula for the average of three test scores is:

Average=Score1+Score2+Score33\text{Average} = \frac{\text{Score}_1 + \text{Score}_2 + \text{Score}_3}{3}

We are given:

  • Score1=87\text{Score}_1 = 87
  • Score2=94\text{Score}_2 = 94
  • Average90\text{Average} \geq 90

Let Score3=x\text{Score}_3 = x, the score she needs on the third test.

So the equation becomes:

87+94+x390\frac{87 + 94 + x}{3} \geq 90

Step 2: Solve the inequality.

  1. Multiply both sides by 3 to eliminate the denominator: 87+94+x27087 + 94 + x \geq 270

  2. Simplify the left side: 181+x270181 + x \geq 270

  3. Subtract 181 from both sides to isolate xx: x270181x \geq 270 - 181 x89x \geq 89

Conclusion:

Melinda needs to score at least 89 on her third test to maintain an average of at least 90.

Would you like more details or have any questions about this solution?

Related Questions:

  1. How do you calculate the average of more than three test scores?
  2. What if Melinda wanted an average higher than 90? How would that change the required score?
  3. How does dropping the lowest score affect the average?
  4. What strategies can help improve test scores consistently?
  5. How do weighted averages differ from simple averages in grade calculations?

Tip: Always double-check the required average calculation by plugging the final score back into the original average formula.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Inequality

Formulas

Average formula

Theorems

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Suitable Grade Level

Grades 6-8