Converting between systems portfolio :

Question

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. Show your work.
Roger is curious to know the total weight of all four sandwich fillings he bought. He weighs the fillings 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 grams? Explain your answer.

Answer 1

To solve Roger's questions, let's go through each part step-by-step.

Step 1: Compare Turkey and Cheese

1. Weight of Turkey: 1.5 kilograms

   • To convert kilograms to pounds, we use the conversion factor \(1 , \text{kilogram} = 2.2 , \text{pounds}\): \[ 1.5 , \text{kilograms} \times 2.2 , \text{pounds/kilogram} = 3.3 , \text{pounds} \]

2. Weight of Cheese: 2.25 pounds

3. Comparison:

   • Turkey: 3.3 pounds
   • Cheese: 2.25 pounds

Since \( 3.3 > 2.25\), Roger purchased more turkey than cheese.

Step 2: Determine Weight of Chicken

Roger wants to buy chicken that weighs more than the beef but less than the turkey.

1. Weight of Beef: 1.25 kilograms

   • Convert to pounds: \[ 1.25 , \text{kilograms} \times 2.2 , \text{pounds/kilogram} = 2.75 , \text{pounds} \]

2. Weight of Turkey: 1.5 kilograms in pounds: (already calculated earlier as \(3.3 , \text{pounds}\))

3. Weight Range for Chicken:

   • Must be greater than 2.75 pounds (beef)
   • Must be less than 3.3 pounds (turkey)

Possible weight for the chicken could be, for instance, 3 pounds (in pounds), since it is more than 2.75 pounds and less than 3.3 pounds.

Step 3: Total Weight Comparison

Total weight of sandwich fillings:

• Turkey: 1.5 kg
• Beef: 1.25 kg
• Cheese: 2.25 lbs (already in pounds)

First, we convert everything to pounds:

• Total weight in kilograms converted to pounds: \[ \text{Turkey in pounds} = 1.5 \times 2.2 = 3.3 , \text{pounds} \] \[ \text{Beef in pounds} = 1.25 \times 2.2 = 2.75 , \text{pounds} \]
• We already have cheese in pounds: \(2.25 , \text{pounds}\)

Now total weight in pounds: \[ 3.3 + 2.75 + 2.25 = 8.3 , \text{pounds} \]

Now convert this total to ounces: \[ \text{Total in ounces} = 8.3 , \text{pounds} \times 16 , \text{ounces/pound} = 132.8 , \text{ounces} \]

Now convert the total weight to grams:

• Total weight in kilograms: \[ 1.5 + 1.25 = 2.75 , \text{kilograms} (for turkey and beef) \]
• Adding cheese in kilograms: \[ \text{Weight of cheese in kg} = \frac{2.25}{2.2} \approx 1.024 , \text{kg} \]
• Total weight in kilograms: \[ 2.75 + 1.024 \approx 3.774 , \text{kilograms} \]

Convert this to grams: \[ \text{Total in grams} = 3.774 \times 1000 = 3774 , \text{grams} \]

Conclusion

Now we have:

• Total in ounces: 132.8 ounces
• Total in grams: 3774 grams

To compare:

• Since \(1 , \text{ounce} \approx 28.35 , \text{grams}\): \[ 132.8 , \text{ounces} \times 28.35 \approx 3768.48 , \text{grams} \]

Final Comparison

• Ounces: 3768.48 grams
• Grams: 3774 grams

Thus, the total weight of the sandwich fillings is a greater number of grams than ounces. The reason is that 8.3 pounds converted to grams (3774g) is slightly more than the converted value of the same weight in ounces (3768.48g).

So in conclusion:

• Weigh of chicken could be: 3.00 pounds
• Total weight comparison: grams are greater than ounces.