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.
Step-by-step 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.
[tex] \dfrac{63 + 62 + 74 + x}{4} [/tex]
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.
[tex] \dfrac{63 + 62 + 74 + x}{4} \ge 70 [/tex]
Now we solve the inequality for x.
Add like terms in the numerator.
[tex] \dfrac{199 + x}{4} \ge 70 [/tex]
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.
