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Problem of the Week
Problem A and Solution
Food Bank Challenge

Problem

Two classes at Whitefish Bay Elementary School took on a challenge to gather donations for a local food bank. Different types of food are worth different amounts of points in the challenge.

The table below lists the donations made by each class.

Class A Class B
\(6\) cans of tuna fish \(3\) boxes of rice
\(5\) jars of peanut butter \(5\) packages of granola bars
\(2\) bags of lentils \(4\) cans of peaches
\(3\) cans of peas \(2\) packages of almonds
\(2\) bags of chips \(7\) boxes of cereal
\(4\) boxes of pasta \(2\) packages of cookies
\(4\) jars of pasta sauce \(3\) boxes of powdered milk

Which class won the challenge? Justify your answer.

Solution

For each class, we calculate how many points they earn for each type of food donated, and summarize in a table.

Class A:

Donation Points per Unit Total Points
\(6\) cans of tuna fish \(4\) \(6 \times 4 = 24\)
\(5\) jars of peanut butter \(3\) \(5 \times 3 = 15\)
\(2\) bags of lentils \(5\) \(2 \times 5 = 10\)
\(3\) cans of peas \(5\) \(3 \times 5 = 15\)
\(2\) bags of chips \(2\) \(2 \times 2 = 4\)
\(4\) boxes of pasta \(1\) \(4 \times 1 = 4\)
\(4\) jars of pasta sauce \(4\) \(4 \times 4 = 16\)

Class B:

Donation Points per Unit Total Points
\(3\) boxes of rice \(5\) \(5 \times 3 = 15\)
\(5\) packages of granola bars \(3\) \(5 \times 3 = 15\)
\(4\) cans of peaches \(5\) \(4 \times 5 = 20\)
\(2\) packages of almonds \(2\) \(2 \times 3 = 6\)
\(7\) boxes of cereal \(4\) \(7 \times 4 = 28\)
\(2\) packages of cookies \(2\) \(2 \times 2 = 4\)
\(3\) boxes of powdered milk \(1\) \(3 \times 1 = 3\)

Now we can add the total points for each class, to determine that Class A made \(24 + 15 + 10 + 15 + 4 + 4 + 16 = 88\) points, and Class B made \(15 + 15 + 20 + 6 + 28 + 4 + 3 = 91\) points.

Therefore, Class B won the challenge.