Final answer:
The acceptable weight of a bag of chips is determined by the absolute value equation |w - 235| ≤ 3, which we solve to find the acceptable weight range between 232 grams and 238 grams, inclusive.
Step-by-step explanation:
The student has asked two questions regarding the weight of bags of chips in a Frito-Lay factory. To tackle this problem, we will write an absolute value equation and then solve it.
Part a
The acceptable range of weight for the bags is from (235 - 3) grams to (235 + 3) grams. We express this using an absolute value equation to represent the maximum deviation from the mean weight of 235g:
|w - 235| ≤ 3
where w represents the weight of the bag of chips.
Part b
To solve the equation |w - 235| ≤ 3, we consider two cases:
w - 235 ≤ 3
-(w - 235) ≤ 3 (which is the same as w - 235 ≥ -3)
Solving the first case:
w ≤ 235 + 3
w ≤ 238
This tells us the heaviest acceptable bag weighs 238 grams.
Solving the second case:
w ≥ 235 - 3
w ≥ 232
This tells us the lightest acceptable bag weighs 232 grams.
Therefore, the heaviest and lightest acceptable bags of chips can weigh between 232 grams and 238 grams, inclusive.