There are two ways to solve this:
First way
In order for 5 quizzes to have an average of 82 we do 82 x 5 = 410 points needed
Adding up what we have 78+72+87+90 = 327 points we've earned so far
Now subtract that from 410. 410-327= 83 - that's what we'll need on quiz #5
Second way - think of this as a tug of war with 82 being the marker in the center of the rope.
72 78 82 87 90
Think of the numbers to the left of 82 as pulling the rope left and the number to the right pulling the rope to the right.
The 72 is pulling left with a force of -10 (from 82) and the 78 is pulling it down -4 (from 82). Total pull to the left is -14 (-10 + -4)
The 87 is pulling the rope right with a force of +5 (from the 82) and 90 is pulling it to the right with a force of +8 (from the 82). Total pull to the right is +13
Since we want the rope marker to stay at 82, we need both side to be pulling equally. But the positive (right) side is one less than we need. So if the last quiz is an 83 that will add +1 to +13 (since 83 is +1 to the right of 82).
Since both sides are pulling with equal force (-14 and +14) the rope will stay at 82 which is what we want.
The tug of war model may seem more
