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Answer :
Final answer:
The students donated 47 jars of 16 oz peanut butter and 35 jars of 28 oz peanut butter to the food bank by setting up and solving a system of linear equations.
Explanation:
The problem requires setting up a system of linear equations with two variables to represent the number of 16 oz jars (let's call this 'x') and the number of 28 oz jars (let's call this 'y') of peanut butter collected by the students.
Step 1: System of Equations
The first equation comes from the total number of jars:
x + y = 82 (Equation 1)
The second equation comes from the total weight of the peanut butter:
16x + 28y = 1876 (Equation 2)
Step 2: Solving the System
We can use substitution or elimination to solve this system. One method is to solve Equation 1 for 'x' and then substitute this into Equation 2.
Step 3: Solution
Solving the system yields:
x = 47 (16 oz jars)
y = 35 (28 oz jars)
Therefore, the students donated 47 jars of 16 oz peanut butter and 35 jars of 28 oz peanut butter to the food bank.
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