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.
\(5\)-point foods: canned meat, canned veggies, canned fruit, lentils, rice
\(4\)-point foods: cereal, crackers, canned beans, canned fish, pasta sauce
\(3\)-point foods: nuts, peanut butter, granola bars
\(2\)-point foods: chips, cookies
\(1\)-point foods: all other non-perishable food items
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.
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.