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Math

QuestionHow much of each ingredient is needed to make 8 brownies from the list for 16 brownies?
Ingredients for 16 brownies: - 13\frac{1}{3} cup butter - 3 ounces unsweetened chocolate - 34\frac{3}{4} cups sugar - 1121 \frac{1}{2} teaspoons vanilla - 2 eggs - 23\frac{2}{3} cup flour

Studdy Solution

STEP 1

Assumptions1. The list of ingredients given is for making16 brownies. . We need to find the amount of each ingredient for making8 brownies.
3. The amounts of the ingredients scale linearly with the number of brownies.

STEP 2

First, we need to find the ratio of the number of brownies we want to make to the number of brownies the recipe makes. This is done by dividing the number of brownies we want to make by the number of brownies the recipe makes.
Ratio=Number of brownies we want to makeNumber of brownies the recipe makesRatio = \frac{Number\, of\, brownies\, we\, want\, to\, make}{Number\, of\, brownies\, the\, recipe\, makes}

STEP 3

Now, plug in the given values for the number of brownies we want to make and the number of brownies the recipe makes to calculate the ratio.
Ratio=816Ratio = \frac{8}{16}

STEP 4

Calculate the ratio.
Ratio=816=12Ratio = \frac{8}{16} = \frac{1}{2}

STEP 5

Now that we have the ratio, we can find the amount of each ingredient needed by multiplying the amount of each ingredient in the recipe by the ratio.
Amount of ingredient needed=Amount of ingredient in recipetimesRatioAmount\, of\, ingredient\, needed = Amount\, of\, ingredient\, in\, recipe \\times Ratio

STEP 6

Plug in the values for the amount of butter in the recipe and the ratio to calculate the amount of butter needed.
Amount of butter needed=13times12Amount\, of\, butter\, needed = \frac{1}{3} \\times \frac{1}{2}

STEP 7

Calculate the amount of butter needed.
Amount of butter needed=13times12=16Amount\, of\, butter\, needed = \frac{1}{3} \\times \frac{1}{2} = \frac{1}{6}

STEP 8

Repeat the process for the other ingredients. For chocolateAmount of chocolate needed=3times12Amount\, of\, chocolate\, needed =3 \\times \frac{1}{2}

STEP 9

Calculate the amount of chocolate needed.
Amount of chocolate needed=3times2=2Amount\, of\, chocolate\, needed =3 \\times \frac{}{2} = \frac{}{2}

STEP 10

For sugarAmount of sugar needed=34times2Amount\, of\, sugar\, needed = \frac{3}{4} \\times \frac{}{2}

STEP 11

Calculate the amount of sugar needed.
Amount of sugar needed=34times=38Amount\, of\, sugar\, needed = \frac{3}{4} \\times \frac{}{} = \frac{3}{8}To make8 brownies, you need 6\frac{}{6} cup of butter, \frac{}{} ounces of chocolate, and 38\frac{3}{8} cups of sugar.

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