Calculating the Fourth Test Score to Achieve an Average of 70

Scenario

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

Understanding the Given Data

• An average of 65 across three tests does not imply each test score was 65.
• For calculation purposes, assume each of the first three test scores is 65.

Calculation Steps

1. Initial Test Scores:
   • Test 1: 65
   • Test 2: 65
   • Test 3: 65
   • These total to 195 (65 + 65 + 65).
2. Formula to Determine Fourth Test Score:
   • To find the needed score on the fourth test (let's call it 'x'), we need the average of four tests to be 70.
   • The formula is:
     [ \frac{65 + 65 + 65 + x}{4} = 70 ]
   • Simplify to:
     [ 195 + x = 280 ]
3. Solving for 'x':
   • Subtract 195 from 280:
     • 280 - 195 = 85
   • Therefore, the student needs to score 85 on the fourth test.

Conclusion

• To achieve an average score of 70 after four tests, the student needs to score 85 on the fourth test.