Calculating Required Grade on Fourth Test

Problem Overview

• A student has an average score of 65 on three tests.
• The goal is to determine the score needed on a fourth test to raise the average to 70.

Key Concepts

Understanding Averages

• An average score of 65 on three tests doesn't mean each test was exactly 65; it’s the sum divided by the number of tests.
• General assumption for simplicity in calculations: each test is considered 65.

Mathematical Approach

• Current average: ((65 + 65 + 65) / 3 = 65)
• New desired average after four tests: 70

Steps to Solve

1. Set up the Equation:

   • Total score after four tests should equal 70 * 4 (since average is sum divided by number of tests).
   • Equation: (65 + 65 + 65 + x = 280) (where x is the score needed on the fourth test).

2. Calculate Current Sum:

   • Sum of the first three test scores:
     • 65 + 65 + 65 = 195

3. Solve for the Unknown (x):

   • Subtract the sum of the first three tests from the total desired sum:
   • 280 (desired total) - 195 (current sum) = 85

4. Result:

   • The student needs to score 85 on the fourth test to achieve an average of 70.

Conclusion

• By using the equation and solving for x, we determined that an 85 on the fourth test is required to attain the desired average.
• This process involves combining knowledge of averages, equation setup, and solving for unknowns.