Answer:
The student needs a minimum score of 81 on the fourth test to ensure a grade of at least a C in the class.
Explanation:
Remember what an average is. (Look at the hint at the bottom of the problem.)
To find the average of a set of numbers, add all the numbers and divide by the number of numbers.
For example, if in a class you took 8 tests, the average of the 8 tests is the sum of the 8 scores divided by 8.
In this case, the student took 3 tests and is taking one more, so in the end there will be 4 scores. The number of tests is 4.
We know 3 of the 4 scores. We don't know the fourth score because he has not taken the test yet, so we use a variable to represent the unknown score. Let's call the score of the fourth test x.
To find the average of the 4 scores, we add them and divide the sum by 4.
The three known scores are 63, 62, 74.
The unknown score is x.
Add all 4 scores: 63 + 62 + 74 + x.
Now we divide the sum of the 4 scores by 4 to find the average of the 4 scores.
The expression above is the average of the 4 scores. We want the average to be at least 70, so we need the average to be greater than or equal to 70.
We get this inequality.
Now we solve the inequality for x.
Add like terms in the numerator.
Multiply both sides by 4.
199 + x = 280
Subtract 199 from both sides.
x = 81
Answer: The student needs a minimum score of 81 on the fourth test to ensure a grade of at least a C in the class.