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Chin canned a number of quart jars and a number of pint jars of tomatoes from his garden. A pint is 16 ounces and a quart is 32 ounces. The number of pints he canned is represented by [tex]\( p \)[/tex], and the number of quarts he canned is represented by [tex]\( q \)[/tex]. Which equation models the scenario if Chin canned a total of 1,280 ounces?

A. [tex]\( 1,280 + 16p = 32q \)[/tex]
B. [tex]\( 1,280 + 32q = 16p \)[/tex]
C. [tex]\( 32q - 16p = 1,280 \)[/tex]
D. [tex]\( 16p + 32q = 1,280 \)[/tex]



Answer :

GinnyAnswer
To determine the correct equation that models the scenario where Chin canned 1,280 ounces of tomatoes in pint and quart jars, let's consider the following:

1. A pint jar contains 16 ounces.
2. A quart jar contains 32 ounces.
3. Let [tex]\( p \)[/tex] represent the number of pint jars.
4. Let [tex]\( q \)[/tex] represent the number of quart jars.
5. The total volume canned is 1,280 ounces.

We need to sum the contributions from pint jars and quart jars to equal the total volume. Each pint jar contributes 16 ounces, and each quart jar contributes 32 ounces. So, the equation should reflect the sum of 16 ounces times the number of pint jars and 32 ounces times the number of quart jars equaling 1,280 ounces.

Step-by-step, we can write this expression as follows:
- The total contribution from the pint jars is [tex]\( 16 \times p \)[/tex] ounces.
- The total contribution from the quart jars is [tex]\( 32 \times q \)[/tex] ounces.
- When these contributions are added together, they should equal the total volume of 1,280 ounces.

Thus, the correct equation to model the scenario is:
[tex]\[ 16p + 32q = 1280 \][/tex]

So, from the given options, the equation that models the scenario is:
[tex]\[ 16 p + 32 q = 1,280 \][/tex]

Therefore, the correct choice is:
[tex]\[ 16 p + 32 q = 1,280 \][/tex]

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