Flynn’s class is raising money for a tree-planting charity by recycling electronics. They have found a local company that will give them \(\$5\) for each pound of cell phone e-waste and \(\$2\) for each pound of computer e-waste.
The school has gathered the following electronics for recycling, but has weighed them in grams instead of pounds.
| Cell Phones | Computers |
|---|---|
| \(10\) uPhones: \(200\) g each | \(5\) Bonobo laptops: \(800\) g each |
| \(5\) Mixel phones: \(100\) g each | \(7\) uPads: \(500\) g each |
Knowing that \(1\) pound is about \(454\) g, estimate how much money Flynn’s class will make. Justify your answer.
Solutions may vary, possibly resulting in different estimations. We will show two different approaches.
Since \(1\) pound is about \(454\) g, we will approximate \(1\) pound as \(500\) g. Then \(2\) pounds is approximately \(1000\) g.
Solution 1
In this solution, we find the total mass of each type of item and then estimate this in pounds before finding the total mass of all items.
Phones:
uPhones: Each uPhone is \(200\) g, so \(10\) uPhones are \(10 \times 200 = 2000\) g. Since \(1000\) g is approximately \(2\) pounds, then \(2000\) g is approximately \(4\) pounds.
Mixel phones: Each Mixel phone is \(100\) g, so \(5\) Mixel phones are \(5 \times 100 = 500\) g, which is approximately \(1\) pound.
This is approximately \(4+1=5\) pounds of cell phone waste. The cell phone e-waste is worth approximately \(\$5 \times 5 = \$25\).
Computers:
Bonobo laptops: Each laptop is \(800\) g, so \(5\) laptops are \(5 \times 800= 4000\) g. Since \(1000\) g is approximately \(2\) pounds, then \(4000\) g is approximately \(4 \times 2 =8\) pounds.
uPads: Each uPad is \(500\) g, which is approximately \(1\) pound, so \(7\) uPads are approximately \(7\) pounds.
This is approximately \(8+7=15\) pounds of computer waste. The computer e-waste is worth approximately \(\$2 \times 15 = \$30\). Therefore the total value is approximately \(\$25 + \$30 = \$55\).
Solution 2
In this solution, we will find the total mass of computer waste and the total mass of cell phone waste, and then estimate these totals in pounds.
Phones:
uPhones: Each uPhone is \(200\) g, so \(10\) uPhones are \(10 \times 200 = 2000\) g.
Mixel phones: Each Mixel phone is \(100\) g, so \(5\) Mixel phones are \(5 \times 100 = 500\) g.
This is \(2000 + 500 = 2500\) g. Since \(500\) g is approximately \(1\) pound and \(1000\) g is approximately \(2\) pounds, then \(2500\) g is approximately \(2+2+1=5\) pounds. The cell phone e-waste is worth approximately \(\$5 \times 5 = \$25\).
Computers:
Bonobo laptops: Each laptop is \(800\) g, so \(5\) laptops are \(5 \times 800= 4000\) g.
uPads: Each uPad is \(500\) g, so \(7\) uPads are \(7 \times 500 = 3500\) g.
This is \(4000 + 3500 = 7500\) g. Since \(500\) g is approximately \(1\) pound and \(1000\) g is approximately \(2\) pounds, then \(7500\) g is approximately \(2\times 7+1=15\) pounds. The computer e-waste is worth approximately \(\$2 \times 15 = \$30\). Therefore the total value is approximately \(\$25 + \$30 = \$55\).