Math

QuestionFind the equation for the acceptable weight range of bags filled with 14 ounces of chocolate, given a tolerance of 0.3 ounces.

Studdy Solution

STEP 1

Assumptions1. The machine fills bags with14 ounces of chocolate. . The bags are not approved for use if they weigh0.3 ounces more or less than the needed weight.

STEP 2

We need to write an equation that represents the highest and lowest weights that will be approved for use. The highest weight is14 ounces plus0. ounces, and the lowest weight is14 ounces minus0. ounces.We can use absolute value to represent this situation because the weight can deviate from the desired weight by0. ounces in either direction. The absolute value of a number is its distance from zero on the number line, regardless of direction. In this case, the "zero" is the desired weight of14 ounces.
The equation will be of the formwa=b|w - a| = bwhere w represents the weight of the bag, a is the desired weight, and b is the maximum deviation from the desired weight.

STEP 3

Substitute the given values into the equation. The desired weight a is14 ounces and the maximum deviation b is0.3 ounces.
w14=0.3|w -14| =0.3This equation represents the highest and lowest weights that will be approved for use. If the absolute value of the difference between the weight of the bag and14 ounces is less than or equal to0.3 ounces, then the bag will be approved for use.

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