Math

QuestionCalculate the total energy in kilocalories for 3 cups of whole milk with 13.36g carbs, 3.38g fat, 6.00g protein.

Studdy Solution

STEP 1

Assumptions1. A cup of whole milk contains13.36 grams of carbohydrate,3.38 grams of fat, and6.00 grams of protein. . The energy values for carbohydrates, fats, and proteins are4,9, and5 kilocalories per gram respectively.
3. We need to find the total energy content in kilocalories of3 cups of whole milk.

STEP 2

First, we need to find the energy content of each component in a cup of milk. We can do this by multiplying the amount of each component by its respective energy value.
Energycarbohydrate=AmountcarbohydratetimesEnergyvaluecarbohydrateEnergy_{carbohydrate} = Amount_{carbohydrate} \\times Energy\, value_{carbohydrate}Energyfat=AmountfattimesEnergyvaluefatEnergy_{fat} = Amount_{fat} \\times Energy\, value_{fat}Energyprotein=AmountproteintimesEnergyvalueproteinEnergy_{protein} = Amount_{protein} \\times Energy\, value_{protein}

STEP 3

Now, plug in the given values for the amount and energy value of each component to calculate the energy content.
Energycarbohydrate=13.36gramstimeskilocalories/gramEnergy_{carbohydrate} =13.36\, grams \\times\, kilocalories/gramEnergyfat=3.38gramstimes9kilocalories/gramEnergy_{fat} =3.38\, grams \\times9\, kilocalories/gramEnergyprotein=6.00gramstimes5kilocalories/gramEnergy_{protein} =6.00\, grams \\times5\, kilocalories/gram

STEP 4

Calculate the energy content of each component.
Energycarbohydrate=13.36gramstimes4kilocalories/gram=53.44kilocaloriesEnergy_{carbohydrate} =13.36\, grams \\times4\, kilocalories/gram =53.44\, kilocaloriesEnergyfat=3.38gramstimes9kilocalories/gram=30.42kilocaloriesEnergy_{fat} =3.38\, grams \\times9\, kilocalories/gram =30.42\, kilocaloriesEnergyprotein=6.00gramstimeskilocalories/gram=30.00kilocaloriesEnergy_{protein} =6.00\, grams \\times\, kilocalories/gram =30.00\, kilocalories

STEP 5

Now that we have the energy content of each component, we can find the total energy content in a cup of milk. This is the sum of the energy content of all components.
Energytotal=Energycarbohydrate+Energyfat+EnergyproteinEnergy_{total} = Energy_{carbohydrate} + Energy_{fat} + Energy_{protein}

STEP 6

Plug in the values for the energy content of each component to calculate the total energy content.
Energytotal=53.44kilocalories+30.42kilocalories+30.00kilocaloriesEnergy_{total} =53.44\, kilocalories +30.42\, kilocalories +30.00\, kilocalories

STEP 7

Calculate the total energy content in a cup of milk.
Energytotal=53.44kilocalories+30.42kilocalories+30.00kilocalories=113.86kilocaloriesEnergy_{total} =53.44\, kilocalories +30.42\, kilocalories +30.00\, kilocalories =113.86\, kilocalories

STEP 8

Now that we have the total energy content in a cup of milk, we can find the total energy content in3 cups of milk. This is done by multiplying the energy content in a cup of milk by the number of cups.
Energy3cups=EnergytotaltimesNumberofcupsEnergy_{3\, cups} = Energy_{total} \\times Number\, of\, cups

STEP 9

Plug in the values for the total energy content and the number of cups to calculate the total energy content in3 cups of milk.
Energy3cups=113.86kilocaloriestimes3Energy_{3\, cups} =113.86\, kilocalories \\times3

STEP 10

Calculate the total energy content in3 cups of milk.
Energy3cups=113.86kilocaloriestimes3=341.58kilocaloriesEnergy_{3\, cups} =113.86\, kilocalories \\times3 =341.58\, kilocaloriesThe total energy content in3 cups of whole milk is341.58 kilocalories.

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