Question

A quality control officer is randomly checking the weights of pumpkin seed bags being filled by an automatic filling machine. Each bag is advertised as weighing 400 grams. A bag must weigh within 2.1 grams in order to be accepted. What is the range of rejected bags, x, for the bags of pumpkin seeds?

Answer 1

`x<397.9 \ grams\\x>397.9 \ grams`

Explanation:

The range of rejected bags is found by summing and subtracting the 400 grams to 2.1 grams, because the second one represent the acceptable margin.

So, we have:

`(400-2.1) \ grams<x<(400+2.1)\ grams\\397.9 \ grams <x<402.1 \ grams`

However, this interval represents the accepted range. The rejected range would be the opposite. Therefore, the asked range is:

`x<397.9 \ grams\\x>397.9 \ grams`

Answer 2

If a bag of pumpkin seeds must weigh within 2.1 grams in order to be accepted, each bags must weigh between (400-2.1) grams and (400+2.1) grams. This means that if a bag weighs less than 397.9 grams (x<397.9) or more than 402.1 grams (x>402.1) it will be rejected. Therefore, 397.9>x>402.1 is the range of rejected bags.