Question

Todd has a new spook of wire like the one pictured. He needs 48 pieces of wire, each 22 feet long. He is estimates that he needs 50:20=1000 feet, and he concludes that 1 spool with 1000 feet will be enough

Answer 1

Answer: 1000 ft will not be enough.

Explanation:

He needs 48 pieces of wire, and each piece of wire must be 22 feet long.

The math that he does is

50*20 instead of 48*22 because it may be easier to do:

But in the math of Todd, he adds two times the smallest number

50*20 = (48 + 2)(22 -2) = 48*22 + 2*22 - 2*48

where 48*22 is the exact number, and the other twos are the errors of the estimation, you can see that the amount that he underestimates (2*48) is bigger than the amount that he overestimates (2*22) so the result that he is obtaining in the multiplication 50*20 is smaller than the one that he actually needs, so 1000ft of cable will not be enough.

You also can do the multiplication: 48*22 = 1056 feet, wich is what he actually needs.