Question

A bag of Hershey's Kisses contains the following information: Serving size: 9 pieces \(=41 \mathrm{~g}\) Calories per serving: 230 Total fat per serving: \(13 \mathrm{~g}\) (a) The bag contains \(2.0\) lbs of Hershey's Kisses. How many Kisses are in the bag? (b) The density of a Hershey's Kiss is \(1.4 \mathrm{~g} / \mathrm{mL}\). What is the volume of a single Hershey's Kiss? (c) How many Calories are in one Hershey's Kiss? (d) Each gram of fat yields 9 Calories when metabolized. What percent of the calories in Hershey's Kisses are derived from fat?

Short answer

199 Kisses; each Kiss is about 3.25 mL, has 25.56 Calories, and 50.9% of these are from fat.

Step-by-step solution

Convert Pounds to Grams

First, we need to convert the weight of the bag from pounds to grams since the serving size information is given in grams. There are 454 grams in one pound. Thus, 2.0 lbs is equal to: \[ 2.0 \text{ lbs} \times 454 \text{ g/lb} = 908 \text{ g} \]

Calculate the Number of Kisses

Since a serving size of 9 pieces of Hershey's Kisses is 41 grams, we can set up a proportion to find how many Kisses are in 908 grams:\[ \frac{9 \text{ Kisses}}{41 \text{ g}} = \frac{x \text{ Kisses}}{908 \text{ g}} \] Solving for \(x\), we find:\[ x = \frac{9 \times 908}{41} \approx 199 \text{ Kisses} \]

Calculate the Volume of One Kiss

The density of one Kiss is given as 1.4 g/mL. With each Kiss weighing approximately \( \frac{41}{9} \) g, we find the volume for one Kiss using the formula:\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{\frac{41}{9}\text{ g}}{1.4 \text{ g/mL}} \approx 3.25 \text{ mL} \]

Calculate Calories Per Kiss

The serving size of 9 pieces has 230 Calories. Hence, one Kiss contains:\[ \text{Calories per Kiss} = \frac{230}{9} \approx 25.56 \text{ Calories} \]

Calculate Calories from Fat

Each Kiss contains \( \frac{13}{9} \) g of fat. Since each gram of fat is worth 9 Calories, the Calories from fat are:\[ \text{Calories from Fat per Kiss} = \frac{13}{9} \times 9 = 13 \text{ Calories} \]

Calculate Percent of Calories from Fat

Using the values from previous steps, the percent of total calories from fat is given by:\[ \text{Percent from Fat} = \left(\frac{13}{25.56}\right) \times 100 \approx 50.9\% \]

Key concepts

Serving Size Calculation

When you're trying to figure out how many pieces of a snack like Hershey's Kisses are in a larger bag, understanding serving size is essential. Each serving size on the package tells you how much product you typically consume in one sitting. For Hershey's Kisses, a serving size is listed as 9 pieces, which equals 41 grams. This information is crucial because it helps you scale up or down depending on the total amount you have.

If you have a bag weighing 2 pounds, you first convert this weight to grams since the serving size is in grams. With 1 pound equaling 454 grams, 2 pounds translates to 908 grams. Knowing this, you can use proportions to determine how many kisses the entire bag contains:

• 9 pieces weigh 41 grams
• Therefore, with a bag weighing 908 grams, the calculation is \[ x = \frac{9 \times 908}{41} \approx 199 \text{ Kisses} \]

This calculation tells you that approximately 199 Kisses are in a 2-pound bag.

Density and Volume Relationship

The relationship between density and volume is key in understanding how much space an object occupies based on its mass. Density is defined as mass per unit volume and is often expressed in terms such as grams per milliliter (g/mL).

For Hershey's Kisses, the density is specified as 1.4 g/mL. Knowing that each serving size (9 Kisses) weighs 41 grams, you can find the mass of a single Kiss by dividing 41 by 9. To find the volume of one Kiss, use the formula for density:

• Volume = Mass / Density
• Mass of one Kiss = 41 grams / 9
• Using the density (1.4 g/mL), the volume calculation becomes \[ \text{Volume} = \frac{\frac{41}{9} \text{ g}}{1.4 \text{ g/mL}} \approx 3.25 \text{ mL} \]

This calculation tells you each Hershey's Kiss occupies an approximate volume of 3.25 mL.

Calories from Fat

Understanding where the calories in your food come from, especially those from fat, helps you make informed dietary choices. Each serving contains 230 calories, with 13 grams of fat per serving. Knowing that each gram of fat provides 9 calories, you can calculate how many calories come from fat in each Kiss.
For one Hershey's Kiss, you initially find how much fat it contains by dividing the total fat by the number of Kisses per serving:

• Fat per Kiss = 13 grams / 9 Kisses
• Calories from Fat per Kiss = (Fat per Kiss) \( \times \) 9 Calories/gram
  After calculating, you find \[ \text{Calories from Fat per Kiss} = \frac{13}{9} \times 9 = 13 \text{ Calories} \] from fat.

Then, to find the percentage of total calories derived from fat in one Kiss, compare the calories from fat to the total calories per Kiss:

• Percent from Fat = (Calories from Fat per Kiss/Calories per Kiss) \( \times \) 100%
• This results in \[ \text{Percent from Fat} = \left(\frac{13}{25.56}\right) \times 100 \approx 50.9\% \]

This means about 50.9% of the calories in a single Hershey's Kiss come from fat, which is useful to know for nutritional balance.