QuestionHow many kilocalories are in 3 cups of whole milk with 13.36g carbs, 3g fat, and 6g protein? Include unit symbol.

Studdy Solution

STEP 1

Assumptions1. One cup of whole milk contains13.36 grams of carbohydrate,8 grams of fat, and6.00 grams of protein. . The energy values for the three food types are as follows Carbohydrate4 kcal/g, Fat9 kcal/g, Protein4 kcal/g.
3. We are asked to find the total energy content in3 cups of whole milk.

STEP 2

First, we need to find the energy content in one cup of whole milk. We can do this by multiplying the amount of each nutrient by its energy value.
$Energy_{carbohydrate} = Amount_{carbohydrate} \\times Energy\, value_{carbohydrate}$ $Energy_{fat} = Amount_{fat} \\times Energy\, value_{fat}$ $Energy_{protein} = Amount_{protein} \\times Energy\, value_{protein}$

STEP 3

Now, plug in the given values for the amount and energy value of each nutrient to calculate the energy content.
$Energy_{carbohydrate} =13.36g \\timeskcal/g$ $Energy_{fat} =8g \\times9kcal/g$ $Energy_{protein} =6.00g \\timeskcal/g$

STEP 4

Calculate the energy content for each nutrient.
$Energy_{carbohydrate} =13.36g \\times4kcal/g =53.44kcal$ $Energy_{fat} =8g \\times9kcal/g =72kcal$ $Energy_{protein} =6.00g \\times4kcal/g =24kcal$

STEP 5

Now that we have the energy content for each nutrient, we can find the total energy content in one cup of whole milk. This is the sum of the energy content of all the nutrients.
$Total\, energy = Energy_{carbohydrate} + Energy_{fat} + Energy_{protein}$

STEP 6

Plug in the values for the energy content of each nutrient to calculate the total energy content.
$Total\, energy =53.44kcal +72kcal +24kcal$

STEP 7

Calculate the total energy content in one cup of whole milk.
$Total\, energy =53.44kcal +72kcal +24kcal =149.44kcal$

STEP 8

Now that we have the total energy content in one cup of whole milk, we can find the total energy content in3 cups of whole milk. This is done by multiplying the energy content in one cup by the number of cups.
$Total\, energy_{3\, cups} = Total\, energy_{1\, cup} \\times Number\, of\, cups$

STEP 9

Plug in the values for the total energy content in one cup and the number of cups to calculate the total energy content in3 cups.
$Total\, energy_{3\, cups} =149.44kcal \\times3$

STEP 10

Calculate the total energy content in3 cups of whole milk.
$Total\, energy_{3\, cups} =149.44kcal \\times3 =448.32kcal$ The3 cups of whole milk contain448.32 kilocalories.

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