A machine is used to fill each of several bags with 16 ounces of sugar. After the bags are filled another machine weighs them. If the bag weighs 0.3 ounces more or less than the desired weight, the bag is reflected. Write this absolute value equation to find the heaviest and lightest bag the machine will approve.
|w-16| < 0.3
Well, it sounds like the sugar-filling machines have a strict weight-limit policy - they're really trying to bag some heavy culprits! Let me calculate this absolute value equation for you:
Let x represent the weight of the bag (in ounces).
The desired weight of each bag is 16 ounces.
Based on the information given, the bag will be approved if it weighs within 0.3 ounces of the desired weight. This can be written as:
|x - 16| ≤ 0.3
This equation basically means that the difference between the weight of the bag and 16 ounces must be less than or equal to 0.3 ounces. If the absolute value of this difference is greater than 0.3 ounces, the bag will be reflected, just like a mirror.
So, to find the heaviest and lightest bags that the machine will approve, you can solve this equation and consider the range of x values that satisfy it.
Let's define the weight of each bag as w (in ounces) and the desired weight as 16 ounces.
To find the absolute value equation that represents the bags the machine will approve, we need to consider the bag weights within the allowable range.
The machine will approve bags that weigh within 0.3 ounces of the desired weight. Therefore, the acceptable range is between 16 - 0.3 and 16 + 0.3, or 15.7 and 16.3 ounces.
Using this information, we can write the absolute value equation as follows:
|w - 16| ≤ 0.3
This equation represents the bag weights that the machine will approve. To find the heaviest and lightest approved bags, we can set up two separate equations:
w - 16 = 0.3 (to find the heaviest bag)
w - 16 = -0.3 (to find the lightest bag)
Solving the first equation for w:
w - 16 = 0.3
w = 16 + 0.3
w = 16.3
Solving the second equation for w:
w - 16 = -0.3
w = 16 - 0.3
w = 15.7
Therefore, the heaviest bag the machine will approve weighs 16.3 ounces, and the lightest bag weighs 15.7 ounces.
To write the absolute value equation for finding the heaviest and lightest bags the machine will approve, we need to consider the desired weight, which is 16 ounces. Let's assign the variable x to represent the weight of a bag.
For the heaviest bag, since the bag can weigh 0.3 ounces more than the desired weight, the equation would be:
x ≤ 16 + 0.3
And for the lightest bag, since the bag can weigh 0.3 ounces less than the desired weight, the equation would be:
x ≥ 16 - 0.3
Thus, the absolute value equation to find the heaviest and lightest bags the machine will approve is:
|x - 16| ≤ 0.3