Question
The density of a certain material is such that it weighs 4 pounds for every 5 fluid ounces of volume. Express this density in kilograms per quart. Round your answer to the nearest tenth.
*Note: you must use these exact conversion factors to get this question right.
Weight / mass Volume
1 pound left parenthesis, lb, right parenthesis(lb) = 16 ounces left parenthesis, oz, right parenthesis(oz) 1 cup left parenthesis, cup, right parenthesis(cup) = 8 fluid ounces left parenthesis, fl oz, right parenthesis(fl oz)
1 ton left parenthesis, ton, right parenthesis(ton) = 2000 pounds left parenthesis, lb, right parenthesis(lb) 1 pint left parenthesis, pt, right parenthesis(pt) = 2 cups left parenthesis, cups, right parenthesis(cups)
1 gram left parenthesis, g, right parenthesis(g) = 1000 milligrams left parenthesis, mg, right parenthesis(mg) 1 quart left parenthesis, qt, right parenthesis(qt) = 2 pints left parenthesis, pt, right parenthesis(pt)
1 kilogram left parenthesis, kg, right parenthesis(kg) = 1000 grams left parenthesis, g, right parenthesis(g) 1 gallon left parenthesis, gal, right parenthesis(gal) = 4 quarts left parenthesis, qt, right parenthesis(qt)
1 ounce left parenthesis, oz, right parenthesis(oz) = 28.35 grams left parenthesis, g, right parenthesis(g) 1 cubic foot left parenthesis, ft³, right parenthesis(ft³) = 7.481 gallons left parenthesis, gal, right parenthesis(gal)
1 pound left parenthesis, lb, right parenthesis(lb) = 0.454 kilograms left parenthesis, kg, right parenthesis(kg) 1 liter left parenthesis, L, right parenthesis(L) = 1000 milliliters left parenthesis, mL, right parenthesis(mL)
1 cubic meter left parenthesis, m³, right parenthesis(m³) = 1000 liters left parenthesis, L, right parenthesis(L)
1 gallon left parenthesis, gal, right parenthesis(gal) = 3.785 liters left parenthesis, L, right parenthesis(L)
1 fluid ounce left parenthesis, fl oz, right parenthesis(fl oz) = 29.574 milliliters left parenthesis, mL, right parenthesis(mL)
*Note: you must use these exact conversion factors to get this question right.
Weight / mass Volume
1 pound left parenthesis, lb, right parenthesis(lb) = 16 ounces left parenthesis, oz, right parenthesis(oz) 1 cup left parenthesis, cup, right parenthesis(cup) = 8 fluid ounces left parenthesis, fl oz, right parenthesis(fl oz)
1 ton left parenthesis, ton, right parenthesis(ton) = 2000 pounds left parenthesis, lb, right parenthesis(lb) 1 pint left parenthesis, pt, right parenthesis(pt) = 2 cups left parenthesis, cups, right parenthesis(cups)
1 gram left parenthesis, g, right parenthesis(g) = 1000 milligrams left parenthesis, mg, right parenthesis(mg) 1 quart left parenthesis, qt, right parenthesis(qt) = 2 pints left parenthesis, pt, right parenthesis(pt)
1 kilogram left parenthesis, kg, right parenthesis(kg) = 1000 grams left parenthesis, g, right parenthesis(g) 1 gallon left parenthesis, gal, right parenthesis(gal) = 4 quarts left parenthesis, qt, right parenthesis(qt)
1 ounce left parenthesis, oz, right parenthesis(oz) = 28.35 grams left parenthesis, g, right parenthesis(g) 1 cubic foot left parenthesis, ft³, right parenthesis(ft³) = 7.481 gallons left parenthesis, gal, right parenthesis(gal)
1 pound left parenthesis, lb, right parenthesis(lb) = 0.454 kilograms left parenthesis, kg, right parenthesis(kg) 1 liter left parenthesis, L, right parenthesis(L) = 1000 milliliters left parenthesis, mL, right parenthesis(mL)
1 cubic meter left parenthesis, m³, right parenthesis(m³) = 1000 liters left parenthesis, L, right parenthesis(L)
1 gallon left parenthesis, gal, right parenthesis(gal) = 3.785 liters left parenthesis, L, right parenthesis(L)
1 fluid ounce left parenthesis, fl oz, right parenthesis(fl oz) = 29.574 milliliters left parenthesis, mL, right parenthesis(mL)
Answers
GPT-4o mini
To find the density of the material in kilograms per quart, we start with the given information that the material weighs 4 pounds for every 5 fluid ounces of volume. We will convert this density step-by-step into kilograms per quart.
### Step 1: Find the weight in kilograms
We have:
- Weight = 4 pounds
Using the conversion factor \(1 \text{ pound} = 0.454 \text{ kilograms}\):
\[
\text{Weight in kilograms} = 4 \, \text{pounds} \times 0.454 \, \frac{\text{kg}}{\text{pound}} = 1.816 \, \text{kg}
\]
### Step 2: Find the volume in quarts
We have:
- Volume = 5 fluid ounces
Now using the conversion:
- \(1 \text{ fluid ounce} = 29.574 \text{ milliliters}\)
- First, convert fluid ounces to milliliters:
\[
\text{Volume in milliliters} = 5 \, \text{fluid ounces} \times 29.574 \, \frac{\text{mL}}{\text{fluid ounce}} = 147.87 \, \text{mL}
\]
Next, we convert milliliters to liters:
\[
\text{Volume in liters} = 147.87 \, \text{mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.14787 \, \text{L}
\]
Finally, we convert liters to quarts using the conversion \(1 \text{ gallon} = 3.785 \text{ L}\) and \(1 \text{ gallon} = 4 \text{ quarts}\):
\[
\text{Volume in quarts} = 0.14787 \, \text{L} \times \frac{1 \text{ gallon}}{3.785 \text{ L}} \times \frac{4 \text{ quarts}}{1 \text{ gallon}}
\]
Calculating this:
\[
= 0.14787 \times \frac{4}{3.785} \approx 0.1573 \, \text{quarts}
\]
### Step 3: Density in kg per quart
Now we can calculate the density:
\[
\text{Density} = \frac{\text{Weight in kg}}{\text{Volume in quarts}} = \frac{1.816 \, \text{kg}}{0.1573 \, \text{quarts}} \approx 11.56 \, \frac{\text{kg}}{\text{quart}}
\]
### Step 4: Round to the nearest tenth
Rounding \(11.56\) to the nearest tenth gives:
\[
\text{Density} \approx 11.6 \, \frac{\text{kg}}{\text{quart}}
\]
Therefore, the density of the material is **11.6 kg per quart**.
### Step 1: Find the weight in kilograms
We have:
- Weight = 4 pounds
Using the conversion factor \(1 \text{ pound} = 0.454 \text{ kilograms}\):
\[
\text{Weight in kilograms} = 4 \, \text{pounds} \times 0.454 \, \frac{\text{kg}}{\text{pound}} = 1.816 \, \text{kg}
\]
### Step 2: Find the volume in quarts
We have:
- Volume = 5 fluid ounces
Now using the conversion:
- \(1 \text{ fluid ounce} = 29.574 \text{ milliliters}\)
- First, convert fluid ounces to milliliters:
\[
\text{Volume in milliliters} = 5 \, \text{fluid ounces} \times 29.574 \, \frac{\text{mL}}{\text{fluid ounce}} = 147.87 \, \text{mL}
\]
Next, we convert milliliters to liters:
\[
\text{Volume in liters} = 147.87 \, \text{mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.14787 \, \text{L}
\]
Finally, we convert liters to quarts using the conversion \(1 \text{ gallon} = 3.785 \text{ L}\) and \(1 \text{ gallon} = 4 \text{ quarts}\):
\[
\text{Volume in quarts} = 0.14787 \, \text{L} \times \frac{1 \text{ gallon}}{3.785 \text{ L}} \times \frac{4 \text{ quarts}}{1 \text{ gallon}}
\]
Calculating this:
\[
= 0.14787 \times \frac{4}{3.785} \approx 0.1573 \, \text{quarts}
\]
### Step 3: Density in kg per quart
Now we can calculate the density:
\[
\text{Density} = \frac{\text{Weight in kg}}{\text{Volume in quarts}} = \frac{1.816 \, \text{kg}}{0.1573 \, \text{quarts}} \approx 11.56 \, \frac{\text{kg}}{\text{quart}}
\]
### Step 4: Round to the nearest tenth
Rounding \(11.56\) to the nearest tenth gives:
\[
\text{Density} \approx 11.6 \, \frac{\text{kg}}{\text{quart}}
\]
Therefore, the density of the material is **11.6 kg per quart**.