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QuestionHow much of each ingredient is needed to make 8 brownies if the original recipe makes 16? Use 13\frac{1}{3} cup butter, 8 oz chocolate, 34\frac{3}{4} cup sugar, 1121 \frac{1}{2} tsp vanilla, 2 eggs, 23\frac{2}{3} cup flour, and find 16\frac{1}{6} cup butter needed.

Studdy Solution

STEP 1

Assumptions1. The given recipe makes16 brownies. . We want to make8 brownies.
3. The quantity of each ingredient is directly proportional to 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.
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 quantity of each ingredient needed for8 brownies. This can be done by multiplying the quantity of each ingredient in the recipe by the ratio.
Quantity for 8 brownies=Quantity in recipetimesRatioQuantity\, for\,8\, brownies = Quantity\, in\, recipe \\times Ratio

STEP 6

Now, plug in the given values for the quantity of butter in the recipe and the ratio to calculate the quantity of butter needed for8 brownies.
Quantity of butter for 8 brownies=13times12Quantity\, of\, butter\, for\,8\, brownies = \frac{1}{3} \\times \frac{1}{2}

STEP 7

Calculate the quantity of butter needed for brownies.
Quantity of butter for  brownies=13times12=16Quantity\, of\, butter\, for\,\, brownies = \frac{1}{3} \\times \frac{1}{2} = \frac{1}{6}So, 16\frac{1}{6} cup(s) of butter is needed to make brownies.

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