Good explanation. I did it very differently:
Given information:
15 boxes
Average of 15 boxes = 8
Therefore, sum of 15 boxes = 15 * 8 = 120 (time saving tip, if you don't know simple multiplications like this, just do 15 * 10 - 15 * 2)
Stem says 5 boxes must be removed and average of 8 must be maintained. Let's plug and play:
A) 1 --> removing 1 10lb box means 4 5-lb boxes must be removed. Total to be removed = 1 * 10 + 4 * 5 = 30 lbs. 120 - 30 = 90
B) 2 --> removing 2 10lb box means 3 5-lb boxes must be removed. Total to be removed = 2 * 10 + 3 * 5 = 35 lbs. 120 - 35 = 85
C) 3 --> removing 3 10lb box means 2 5-lb boxes must be removed. Total to be removed = 3 * 10 + 2 * 5 = 40 lbs. 120 - 40 = 80
D) 4 --> removing 4 10lb box means 1 5-lb boxes must be removed. Total to be removed = 4 * 10 + 1 * 5 = 45 lbs. 120 - 45 = 75
E) 5 --> removing 5 10lb box means 0 5-lb boxes must be removed. Total to be removed = 5 * 10 + 0 * 5 = 50 lbs. 120 - 50 = 70
Quick glance reveals that C will be answer as none others are easily divisible by 8. Could this be wrong and does it warrant a check? Yep - but I would leave it here and move on in the interest of time.
You may disagree with this approach, but it's a 40 second solution.