Mr. Feng conducted five math tests. Trinity had completed four tests and scored 79, 78, 82, and 75. She wanted to achieve an average of 80% in her math tests. Write an inequality to find the minimum score Trinity can make on the fifth test in order to score an 80% for all the tests combined?
(79 + 78 + 82 + 75 + x) / 5 >= 80
78
To find the minimum score Trinity can make on the fifth test in order to achieve an average of 80%, we need to set up an inequality.
Let's denote the score Trinity obtains on the fifth test as "x".
To find the average of all five tests, we need to sum up the scores of all the tests (including the fifth test) and then divide by the total number of tests (which is 5 in this case).
The sum of all the scores on the four tests Trinity has already taken is: 79 + 78 + 82 + 75 = 314.
To achieve an average of 80% for all five tests, the sum of all five scores divided by 5 should be equal to 80%. In mathematical notation, this can be written as:
(314 + x) / 5 = 80
Now we can solve this equation for x to find the minimum score Trinity needs on the fifth test.
Multiply both sides of the equation by 5 to eliminate the denominator:
314 + x = 400
Next, subtract 314 from both sides of the equation:
x = 400 - 314
Simplifying the right side, we have:
x = 86
Therefore, the minimum score Trinity can make on the fifth test in order to score an average of 80% for all the tests combined is 86.
The inequality representation of this solution would be:
x ≥ 86