Roger also wants to make sandwiches for his guests. He buys the following sandwich fillings:
1.5 kilograms of turkey
1.25 kilograms of beef
2.25 pounds of cheese
3 pounds of chicken
Roger is curious to know the total weight of all four sandwich fillings he bought. He weighs it twice, once using ounces and once using grams. If 16 ounces = 1 pound and 1,000 grams = 1 kilogram, will the total weight of the sandwich fillings be a greater number of ounces or a greater number of kilograms? Explain your answer.
Let's convert the turkey and beef weights from kilograms to pounds to standardize the unit of measurement. Then we will add all the fillings together in pounds and convert that to ounces. In parallel, we'll convert pounds to grams for all fillings and add the weight in kilograms and grams to compare.
1. Converting turkey and beef from kilograms to pounds (since 1 kilogram is approximately 2.20462 pounds):
Turkey: 1.5 kg * 2.20462 = 3.30693 pounds
Beef: 1.25 kg * 2.20462 = 2.755775 pounds
2. Total weight of fillings in pounds:
3.30693 (turkey) + 2.755775 (beef) + 2.25 (cheese) + 3 (chicken) = 11.312705 pounds
3. Converting the total weight in pounds to ounces:
11.312705 pounds * 16 ounces/pound = 180.80328 ounces
Now, we will convert the cheese and chicken from pounds to grams to compare which is greater.
1. Converting chicken and cheese from pounds to grams (since 1 pound is approximately 453.59237 grams):
Cheese: 2.25 pounds * 453.59237 = 1020.5928325 grams
Chicken: 3 pounds * 453.59237 = 1360.77711 grams
2. Total weight of fillings in grams:
1020.5928325 (cheese) + 1360.77711 (chicken) + 1500 (turkey) + 1250 (beef) = 5132.370 grams
3. Converting the total weight in grams to kilograms:
5132.370 grams / 1000 = 5.132370 kilograms
Now we compare the two:
- Ounces: 180.80328
- Kilograms: 5.132370
5.132370 kilograms * 1000 = 5132.370 grams
Now, it's important to notice that we are being asked to compare ounces and kilograms – which are two different units of measurement for weight.
To properly compare them, we must either convert ounces to grams or kilos to ounces. Let's convert kilograms to grams first.
5.132370 kilograms * 1000 grams/kilogram = 5132.370 grams
Since we have the total weight in ounces and in grams, let's compare ounces to grams:
- 180.80328 ounces
- 5132.370 grams
Now, to make a fair comparison, we need to convert ounces to grams or vice versa. Since we've already been given that 1 pound equals 453.59237 grams and there are 16 ounces to a pound, we can determine the grams per ounce:
453.59237 grams/pound / 16 ounces/pound = 28.3495228125 grams/ounce
Now, let's convert ounces to grams:
180.80328 ounces * 28.3495228125 grams/ounce ≈ 5127.876 grams
Now, for the final comparison in grams:
- Ounces converted to grams: 5127.876 grams
- Kilograms converted to grams: 5132.370 grams
As you can see, the total weight in grams, which comes from the kilograms, is slightly more. This difference is due to rounding errors in the conversion process. Nevertheless, Roger has a greater number of grams compared to the number of ounces. However, since the question is asking to compare ounces to kilograms, we now need to convert the ounces to kilograms for the final answer.
The conversion from ounces to kilograms is established by the fact that there are 35.274 ounces in a kilogram.
So the conversion for the total weight from ounces to kilograms would be:
180.80328 ounces / 35.274 ounces/kilogram = 5.127 kilograms (approximately)
Now we have the final comparison:
- Ounces converted to kilograms: ~5.127 kilograms
- Total weight in kilograms: 5.132370 kilograms
The number for kilograms remains greater. Roger will have a greater number of grams, and therefore also a greater number of kilograms, when he weighs all the sandwich fillings.