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QuestionCalculate the total energy in kJ for 4 cups of whole milk with 17.86 g carbs, 3.17 g fat, and 3.31 g protein.

Studdy Solution

STEP 1

Assumptions1. One cup of whole milk contains17.86 grams of carbohydrate,3.17 grams of fat, and3.31 grams of protein. . The energy values for carbohydrates, fats, and proteins are17 kJ/g,38 kJ/g, and17 kJ/g respectively.
3. We are asked to find the total energy in4 cups of whole milk.

STEP 2

First, we need to calculate the energy contribution from each nutrient in one cup of milk. We can do this by multiplying the amount of each nutrient by its respective energy value.
Energycarbohydrate=AmountcarbohydratetimesEnergy valuecarbohydrateEnergy_{carbohydrate} = Amount_{carbohydrate} \\times Energy\, value_{carbohydrate}Energyfat=AmountfattimesEnergy valuefatEnergy_{fat} = Amount_{fat} \\times Energy\, value_{fat}Energyprotein=AmountproteintimesEnergy valueproteinEnergy_{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 contribution from each nutrient.
Energycarbohydrate=17.86 gtimes17 kJ/gEnergy_{carbohydrate} =17.86\, g \\times17\, kJ/gEnergyfat=3.17 gtimes38 kJ/gEnergy_{fat} =3.17\, g \\times38\, kJ/gEnergyprotein=3.31 gtimes17 kJ/gEnergy_{protein} =3.31\, g \\times17\, kJ/g

STEP 4

Calculate the energy contribution from each nutrient.
Energycarbohydrate=17.86 gtimes17 kJ/g=303.62 kJEnergy_{carbohydrate} =17.86\, g \\times17\, kJ/g =303.62\, kJEnergyfat=3.17 gtimes38 kJ/g=120.46 kJEnergy_{fat} =3.17\, g \\times38\, kJ/g =120.46\, kJEnergyprotein=3.31 gtimes17 kJ/g=56.27 kJEnergy_{protein} =3.31\, g \\times17\, kJ/g =56.27\, kJ

STEP 5

Now that we have the energy contribution from each nutrient, we can find the total energy in one cup of milk. This is the sum of the energy contributions from carbohydrates, fats, and proteins.
Energytotal=Energycarbohydrate+Energyfat+EnergyproteinEnergy_{total} = Energy_{carbohydrate} + Energy_{fat} + Energy_{protein}

STEP 6

Plug in the values for the energy contributions from carbohydrates, fats, and proteins to calculate the total energy in one cup of milk.
Energytotal=303.62 kJ+120.46 kJ+56.27 kJEnergy_{total} =303.62\, kJ +120.46\, kJ +56.27\, kJ

STEP 7

Calculate the total energy in one cup of milk.
Energytotal=303.62 kJ+120.46 kJ+56.27 kJ=480.35 kJEnergy_{total} =303.62\, kJ +120.46\, kJ +56.27\, kJ =480.35\, kJ

STEP 8

Now that we have the total energy in one cup of milk, we can find the total energy in4 cups of milk. This is4 times the energy in one cup of milk.
Energy4 cups=4timesEnergytotalEnergy_{4\,cups} =4 \\times Energy_{total}

STEP 9

Plug in the value for the total energy in one cup of milk to calculate the total energy in4 cups of milk.
Energy4 cups=4times480.35 kJEnergy_{4\,cups} =4 \\times480.35\, kJ

STEP 10

Calculate the total energy in4 cups of milk.
Energy4 cups=4times480.35 kJ=192.4 kJEnergy_{4\,cups} =4 \\times480.35\, kJ =192.4\, kJThe total energy in4 cups of whole milk is192.4 kilojoules.

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