To determine the correct equation that models the scenario where Chin canned a certain number of pints [tex]\( p \)[/tex] and quarts [tex]\( q \)[/tex] resulting in a total of 1,280 ounces, let's break it down step-by-step:
1. Identify the Ounces for Each Type of Jar:
- A pint (represented by [tex]\( p \)[/tex]) is 16 ounces.
- A quart (represented by [tex]\( q \)[/tex]) is 32 ounces.
2. Calculate the Total Ounces:
- The total ounces from pints is [tex]\( 16 \times p \)[/tex].
- The total ounces from quarts is [tex]\( 32 \times q \)[/tex].
3. Form the Equation:
- The total number of ounces canned from both pints and quarts combined is equal to 1,280 ounces.
- Therefore, the sum of the ounces from pints and quarts should equal 1,280.
The equation that models this scenario is:
[tex]\[ 16p + 32q = 1,280 \][/tex]
This equation accurately states that the total ounces from the number of pints and quarts equals 1,280 ounces.
Thus, the correct equation is:
[tex]\[ 16p + 32q = 1,280 \][/tex]
