Sure, let's solve this step-by-step.
Given: A crate of medicine with a density of 2,050 kilograms per cubic meter (kg/m³).
To find: The crate's density in pounds per cubic foot (lb/ft³).
### Step 1: Use the given density
We start with the given density:
[tex]\[
\frac{2050 \, \text{kg}}{1 \, \text{m}^3}
\][/tex]
### Step 2: Convert kilograms to pounds
We use the conversion factor: [tex]\(1 \, \text{kg} = 2.2 \, \text{lb}\)[/tex]:
[tex]\[
2050 \, \text{kg} \times 2.2 \, \frac{\text{lb}}{\text{kg}} = 2050 \times 2.2 \, \text{lb}
\][/tex]
Thus,
[tex]\[
2050 \, \text{kg} = 4510 \, \text{lb}
\][/tex]
### Step 3: Convert cubic meters to cubic feet
We use the conversion factor: [tex]\(1 \, \text{m}^3 = 35.3 \, \text{ft}^3\)[/tex]:
[tex]\[
\frac{1 \, \text{m}^3}{35.3 \, \text{ft}^3}
\][/tex]
Thus,
[tex]\[
\frac{4510 \, \text{lb}}{35.3 \, \text{ft}^3}
\][/tex]
### Step 4: Calculate the density in pounds per cubic foot
Now we divide 4510 lb by 35.3 ft³ to convert the units:
[tex]\[
\frac{4510 \, \text{lb}}{35.3 \, \text{ft}^3} \approx 127.76 \, \frac{\text{lb}}{\text{ft}^3}
\][/tex]
### Final Answer
The crate's density in pounds per cubic foot, rounded to the nearest hundredth, is:
[tex]\[
127.76 \, \frac{\text{lb}}{\text{ft}^3}
\][/tex]
So, filling in the missing steps and blanks, we have:
[tex]\[
\frac{2050 \, \text{kg}}{1 \, \text{m}^3} \times 2.2 \, \frac{\text{lb}}{\text{kg}} \times \frac{1 \, \text{m}^3}{35.3 \, \text{ft}^3} = 127.76 \, \frac{\text{lb}}{\text{ft}^3}
\][/tex]
