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Math

QuestionHow much of each ingredient is needed to make 8 brownies from the list for 16 brownies?
Ingredients: - 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
Find the amount of butter needed.

Studdy Solution

STEP 1

Assumptions1. The given list of ingredients is for making16 brownies. . We need to find the quantity of each ingredient needed to make8 brownies.
3. The quantities of ingredients needed are 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 (8) to the number of brownies the recipe makes (16).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

implify 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 to make8 brownies. We do this by multiplying the quantity of each ingredient in the recipe by the ratio.
For butterButter needed=Quantity of butter in recipetimesRatioButter\, needed = Quantity\, of\, butter\, in\, recipe \\times Ratio

STEP 6

Plug in the values for the quantity of butter in the recipe and the ratio to calculate the amount of butter needed.
Butter needed=13times12Butter\, needed = \frac{1}{3} \\times \frac{1}{2}

STEP 7

Calculate the amount of butter needed.
Butter needed=13times12=16Butter\, needed = \frac{1}{3} \\times \frac{1}{2} = \frac{1}{6}So, 16\frac{1}{6} cup of butter is needed to make brownies.

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