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 $p$, and the number of quarts he canned is represented by $q$. Which equation models the scenario if Chin canned a total of 1,280 ounces?
A. $1,280+16 p=32 q$
B. $1,280+32 q=16 p$
C. $32 q-16 p=1,280$
D. $16 p+32 q=1,280
Answer (1)
The problem describes a scenario where Chin canned tomatoes in pint and quart jars, with a total of 1,280 ounces. The equation that models this scenario is found by summing the total ounces from pint jars ( 16 p ) and quart jars ( 32 q ) and setting it equal to 1,280. The final equation is: 16 p + 32 q = 1 , 280 .
Explanation
Understanding the Problem Let's analyze the problem. Chin canned tomatoes in pint and quart jars. We know that a pint is 16 ounces and a quart is 32 ounces. We are given the number of pints as p and the number of quarts as q . The total amount canned is 1,280 ounces. Our goal is to find the equation that represents this scenario.
Ounces from Pint Jars First, we need to determine the total ounces from the pint jars. Since each pint jar contains 16 ounces, the total ounces from p pint jars is 16 p .
Ounces from Quart Jars Next, we need to determine the total ounces from the quart jars. Since each quart jar contains 32 ounces, the total ounces from q quart jars is 32 q .
Total Ounces Equation The sum of the ounces from the pint jars and the quart jars must equal the total ounces canned, which is 1,280 ounces. Therefore, the equation that models this scenario is: 16 p + 32 q = 1280
Matching the Equation Now, we compare our derived equation with the given options. The equation 16 p + 32 q = 1280 matches the fourth option.
Examples
Imagine you're organizing a pantry and need to calculate the total volume of canned goods. If you have 'p' cans of 16-ounce beans and 'q' cans of 32-ounce soup, this equation helps you determine if they all fit within a 1280-ounce storage limit. This is a practical way to ensure you don't overstock and can manage your pantry efficiently. Understanding how to set up and solve such equations is useful in everyday resource management.
