To solve this problem, we'll start by understanding the given data and the relationship it describes.
The sports drink is advertised as containing 16 fluid ounces, but the actual amount can vary by up to 0.32 fluid ounces. We need to set up an equation to describe the maximum and minimum possible amounts.
Given:
- [tex]\( x \)[/tex] is the amount of fluid ounces in a bottle.
- The amount varies by [tex]\( 0.32 \)[/tex] ounces.
This variability can be expressed with the following absolute value equation:
[tex]\[ |x - 16| = 0.32 \][/tex]
This equation captures that the deviation from 16 ounces (the advertised amount) is at most 0.32 ounces.
To solve for the actual values, we should consider the two possible scenarios which come from solving the absolute value equation:
1. Positive deviation: [tex]\( x - 16 = 0.32 \)[/tex]
2. Negative deviation: [tex]\( x - 16 = -0.32 \)[/tex]
We solve these algebraically:
1. Positive deviation:
[tex]\[ x - 16 = 0.32 \][/tex]
Adding 16 to both sides:
[tex]\[ x = 16 + 0.32 \][/tex]
[tex]\[ x = 16.32 \][/tex]
Therefore, the maximum amount is [tex]\( 16.32 \)[/tex] fluid ounces.
2. Negative deviation:
[tex]\[ x - 16 = -0.32 \][/tex]
Adding 16 to both sides:
[tex]\[ x = 16 - 0.32 \][/tex]
[tex]\[ x = 15.68 \][/tex]
Therefore, the minimum amount is [tex]\( 15.68 \)[/tex] fluid ounces.
Thus, the minimum and maximum amounts are:
- Minimum amount: [tex]\( 15.68 \)[/tex] fluid ounces
- Maximum amount: [tex]\( 16.32 \)[/tex] fluid ounces
The correct answer derived from the given information is:
- For the minimum amount, we found [tex]\( x = 15.68 \)[/tex] fluid ounces.
And the equations used to model the variability are:
[tex]\[ |x - 16| = 0.32 \][/tex]
So, the final results are:
- Minimum amount: [tex]\( 15.68 \)[/tex] fluid ounces
- Maximum amount: [tex]\( 16.32 \)[/tex] fluid ounces
