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 wants to know if he purchased more turkey or more cheese. Use the
conversion ratio 1 kilogram = about 2.2 pounds to determine the correct answer.
Show your work.
Roger discovers that he needs to buy some chicken as well. He buys an amount of
chicken that weighs more than the beef he bought and less than the turkey he
bought. Give an amount in pounds that the chicken could weigh, rounded to the
nearest hundredth of a pound.
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 the weights of the turkey and beef from kilograms to pounds:
Turkey weight: 1.5 kg * 2.2 pounds/kg = 3.3 pounds
Beef weight: 1.25 kg * 2.2 pounds/kg = 2.75 pounds
Next, we can compare the weights of the turkey and cheese in pounds:
Turkey weight: 3.3 pounds
Cheese weight: 2.25 pounds
The turkey weighs more than the cheese.
For the weight of the chicken, it is between the beef and the turkey. Therefore, it could weigh anywhere between 2.75 pounds (the weight of the beef) and 3.3 pounds (the weight of the turkey).
To determine the total weight of all four sandwich fillings, we need to convert the weights of the turkey, beef, cheese, and chicken (which we just calculated) to ounces and grams.
Turkey weight in ounces: 3.3 pounds * 16 ounces/pound = 52.8 ounces
Beef weight in ounces: 2.75 pounds * 16 ounces/pound = 44 ounces
Cheese weight in ounces: 2.25 pounds * 16 ounces/pound = 36 ounces
Turkey weight in grams: 3.3 pounds * 454 grams/pound = 1498.2 grams
Beef weight in grams: 2.75 pounds * 454 grams/pound = 1247 grams
Cheese weight in grams: 2.25 pounds * 454 grams/pound = 1021.5 grams
The total weight in ounces is 52.8 ounces + 44 ounces + 36 ounces + the weight of the chicken.
The total weight in grams is 1498.2 grams + 1247 grams + 1021.5 grams + the weight of the chicken.
Comparing the conversion ratios, 16 ounces is greater than 1 kilogram and 1,000 grams is less than 1 kilogram. Therefore, the total weight of the sandwich fillings will be a greater number of ounces than kilograms.
To determine if Roger purchased more turkey or more cheese, we need to convert the given weights into the same unit (pounds or kilograms). We'll use the conversion ratio 1 kilogram = about 2.2 pounds.
Turkey weight: 1.5 kilograms
Turkey weight in pounds: 1.5 kilograms * 2.2 pounds/kilogram = 3.3 pounds
Cheese weight: 2.25 pounds
Comparing the weights, we can see that Roger purchased more cheese (2.25 pounds) than turkey (3.3 pounds).
Next, let's find the weight range for the chicken that Roger bought. We know that the chicken weighs more than the beef (1.25 kilograms) and less than the turkey (1.5 kilograms). We'll convert the given weights into pounds for easier comparison.
Beef weight: 1.25 kilograms * 2.2 pounds/kilogram = 2.75 pounds
The chicken weight could range from 2.75 pounds (more than beef) to 3.3 pounds (less than or equal to turkey).
Therefore, rounded to the nearest hundredth of a pound, the chicken could weigh between 2.75 and 3.3 pounds.
Lastly, let's compare the total weight of the sandwich fillings in ounces and grams.
Using ounces:
Turkey weight: 3.3 pounds * 16 ounces/pound = 52.8 ounces
Beef weight: 1.25 kilograms * 2.2 pounds/kilogram * 16 ounces/pound = 35.2 ounces
Cheese weight: 2.25 pounds * 16 ounces/pound = 36 ounces
Chicken weight (average): (2.75 pounds + 3.3 pounds) / 2 * 16 ounces/pound ≈ 95.2 ounces
Total weight in ounces: 52.8 + 35.2 + 36 + 95.2 = 219.2 ounces
Using grams:
Turkey weight: 1.5 kilograms * 1000 grams/kilogram = 1500 grams
Beef weight: 1.25 kilograms * 1000 grams/kilogram = 1250 grams
Cheese weight: 2.25 pounds * 16 ounces/pound * 28.35 grams/ounce = 1275.3 grams
Chicken weight (average): (2.75 pounds + 3.3 pounds) / 2 * 16 ounces/pound * 28.35 grams/ounce ≈ 3402.69 grams
Total weight in grams: 1500 + 1250 + 1275.3 + 3402.69 = 7437.99 grams
Comparing the two measurements, the total weight of the sandwich fillings is a greater number in grams (7437.99 grams) than in ounces (219.2 ounces).
Therefore, the total weight of the sandwich fillings is a greater number of grams.
To determine if Roger purchased more turkey or more cheese, we need to convert the weights to a common unit, either pounds or kilograms. However, in this case, we are given a conversion ratio from kilograms to pounds.
1 kilogram is approximately 2.2 pounds.
Roger purchased 1.5 kilograms of turkey and 2.25 pounds of cheese.
To determine the weight of the turkey in pounds, we multiply the weight in kilograms by the conversion ratio:
1.5 kilograms * 2.2 pounds/kilogram = 3.3 pounds
So, Roger purchased 3.3 pounds of turkey.
Comparing the weights, we can see that Roger purchased more turkey (3.3 pounds) than cheese (2.25 pounds).
Now let's consider the weight of the chicken Roger bought. We know that it weighs more than the beef (1.25 kilograms) and less than the turkey (1.5 kilograms).
To find the weight in pounds, we need to use the conversion ratio: 1 kilogram is approximately 2.2 pounds.
Let's consider the range between the beef and the turkey weights:
1.25 kilograms * 2.2 pounds/kilogram = 2.75 pounds (beef weight in pounds)
1.5 kilograms * 2.2 pounds/kilogram = 3.3 pounds (turkey weight in pounds)
So, the weight of the chicken can be any value between 2.76 pounds (exclusive) and 3.3 pounds (exclusive), rounded to the nearest hundredth of a pound.
Next, let's determine whether the total weight of the four sandwich fillings will be greater in ounces or kilograms.
The conversion ratios we have are:
16 ounces = 1 pound
1,000 grams = 1 kilogram
Roger wants to know the total weight in ounces and kilograms.
To convert the weight of the sandwich fillings to ounces, we need to use the conversion ratio: 1 pound equals 16 ounces.
First, let's convert the total weight to pounds:
Turkey: 3.3 pounds
Beef: 1.25 kilograms * 2.2 pounds/kilogram = 2.75 pounds
Cheese: 2.25 pounds
Total weight in pounds: 3.3 + 2.75 + 2.25 = 8.3 pounds
Now, convert the total weight in pounds to ounces:
8.3 pounds * 16 ounces/pound = 132.8 ounces
The total weight of the sandwich fillings in ounces is 132.8 ounces.
Now, let's convert the total weight to kilograms. The total weight is already in pounds, so we need to convert it from pounds to kilograms. We use the conversion ratio: 1 pound is approximately 0.45 kilograms.
Total weight in pounds: 8.3 pounds
Now, convert the total weight in pounds to kilograms:
8.3 pounds * 0.45 kilograms/pound = 3.735 kilograms
The total weight of the sandwich fillings in kilograms is 3.735 kilograms.
Therefore, the total weight of the sandwich fillings is a greater number in kilograms (3.735 kilograms) than in ounces (132.8 ounces).