Heather already has grades in 3 math tests given as 80, 75, and 86. she needs to write a fourth test and wants an average score of at least 82. That means she wants her next average score to be either 82 or any score above 82. In other words her next average should be "greater than or equal to" 82.
If the next score is given as x (unknown) then her average can be calculated as follows;
[80 + 75 + 86 + x]/4
[80 + 75 + 86 + x]/4 ≥ 82
(This is derived from the formula for calculating an average which is
Average = [Summation of observed data]/Number of observed data
[241 + x]/4 ≥ 82
By cross multiplying you now have
241 + x ≥ 82 * 4
241 + x ≥ 328
Subtract 241 from both sides of the equation
x ≥ 87
The result shows that Heather must score at least 87 points (and nothing less) in her next test in order for her to have an average of at least 82.