Answer
a) $x\geq74$
b) $x\geq37$
Work Step by Step
The limits for a grade of B are given, so we can use them to find the least score to get a grade of B:
$\frac{68+82+87+89+x}{5}=80$
Now, solve for x:
$\frac{68+82+87+89+x}{5}\cdot 5=80\cdot 5$
$68+82+87+89+x=400$
$326+x=400$
$326+x-326=400-326$
$x=74$
74 is the lowest score needed to get a B, and it can be represented as:
$x\geq74$
If the fifth test counts double, half of the lowest score found is needed to get a B:
$2x\geq74$
$2x/2\geq74/2$
$x\geq37$
