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
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.
First, let's convert all the weights into a common unit so we can add them up. We have the weight of turkey and beef in kilograms, and the weight of the cheese in pounds. First, let's convert the cheese weight to ounces, as we know the relationship between pounds and ounces, and then we can decide on whether to convert everything to grams or ounces for the final comparison.
We are given the conversions:
- 1 pound = 16 ounces
- 1 kilogram = 1,000 grams
Let's begin by converting the weight of the cheese from pounds to ounces.
Cheese: 2.25 pounds * 16 ounces/pound = 36 ounces
Now, we'll convert kilograms to grams for turkey and beef, because this will help us compare kilograms to ounces.
Turkey: 1.5 kilograms * 1,000 grams/kilogram = 1,500 grams
Beef: 1.25 kilograms * 1,000 grams/kilogram = 1,250 grams
Let's sum the weights in grams to see the total weight in kilograms:
Total weight in grams = 1,500 grams (turkey) + 1,250 grams (beef) = 2,750 grams
Since 1,000 grams = 1 kilogram, we can convert this to kilograms:
Total weight in kilograms = 2,750 grams / 1,000 grams/kilogram = 2.75 kilograms
Now let's compare this to ounces. We already know the weight of cheese in ounces:
Total weight in ounces (cheese only) = 36 ounces
However, because the question is asking whether the total weight of all the sandwich fillings will be a greater number in ounces or kilograms, we'd need to convert either the weight of turkey and beef into ounces or convert the weight of cheese into grams to make a proper comparison.
Since we've already added the turkey and beef weights in grams, let's convert the cheese weight to grams to finish the comparison.
Cheese in grams: 36 ounces * 28.3495 grams/ounce ≈ 1,020 grams
Now we add all the weights in grams:
Total weight in grams = 1,500 grams (turkey) + 1,250 grams (beef) + 1,020 grams (cheese) = 3,770 grams
So now we clearly see that the total weight in grams is 3,770 grams, which is equivalent to 3.77 kilograms. This number is much larger than the 36 ounces we have for just the cheese in ounces.
Remember that we're asked whether the total weight of all sandwich fillings will be a greater number in ounces or kilograms. To further clarify, if we were to convert the turkey and beef into ounces, the grams would translate to a greater number of ounces because 1 gram = 0.03527396 ounces, and we have thousands of grams. Therefore, we don't even need to do the conversion to know that the total weight in ounces will be larger because there are more ounces in a gram.
In conclusion, without further conversion, it is clear that the greater number will be in ounces, not in kilograms, because the conversion factor from grams to ounces (1 gram = 0.03527396 ounces) will result in a greater numerical value in ounces.