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Assume the density of Karo syrup is [tex]1.37 \, \text{g/mL}[/tex]. What is the volume, in cups, of [tex]2.75 \, \text{lbs}[/tex] of Karo syrup?

Answer :

Sure, let's solve this step by step!

1. Convert the Mass from Pounds to Grams:
- We start with 2.75 pounds of Karo syrup.
- The conversion factor is [tex]\(1 \text{ pound} = 453.592 \text{ grams}\)[/tex].

[tex]\[
\text{Mass in grams} = 2.75 \times 453.592 = 1247.378 \text{ grams}
\][/tex]

2. Calculate the Volume in Milliliters:
- We know the density of Karo syrup is [tex]\(1.37 \text{ g/mL}\)[/tex].
- Density is defined as mass per unit volume, which can be represented by the formula:

[tex]\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\][/tex]

- Rearranging to find the volume:

[tex]\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\][/tex]

- Plugging in the values:

[tex]\[
\text{Volume in mL} = \frac{1247.378 \text{ grams}}{1.37 \text{ g/mL}} \approx 910.495 \text{ mL}
\][/tex]

3. Convert the Volume to Cups:
- One cup is equal to 237 milliliters.

[tex]\[
\text{Volume in cups} = \frac{910.495 \text{ mL}}{237 \text{ mL/cup}} \approx 3.842 \text{ cups}
\][/tex]

So, the volume of 2.75 pounds of Karo syrup is approximately 3.842 cups.

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