Lucy wants to be exempt from her semester exam. In order for that to happen, she has to average an 85 over 3 test grades. Her first 2 test grades were 81 and 86. What does Lucy need to make on her third test in order to have an exact average of 85 and be exempt from her exam?
total points for an 85 average: 85*3 = 255
Points so far: 81+86 = 167
So, haw many does she still need?
(85 * 3) - (81 + 86) = ?
To find out what Lucy needs to make on her third test in order to have an average of 85, we can use the formula for average:
Average = (Sum of all test grades) / (Number of test grades)
In this case, the average (85) is given, and the sum of the first two test grades (81 and 86) is known. Let's call the grade Lucy needs to make on her third test "x".
So, we can set up the equation:
(81 + 86 + x) / 3 = 85
Now, let's solve the equation step by step to find the value of "x".
1. Multiply both sides of the equation by 3 to eliminate the denominator:
81 + 86 + x = 255
2. Combine like terms on the left side of the equation:
167 + x = 255
3. Subtract 167 from both sides of the equation:
x = 255 - 167
4. Solve the equation:
x = 88
Therefore, Lucy needs to make an 88 on her third test in order to have an exact average of 85 and be exempt from her exam.