Math

QuestionDetermine the ingredient amounts for 12 brownies based on a recipe for 16 brownies.

Studdy Solution

STEP 1

Assumptions1. The recipe given is for making16 brownies. . We want to adjust the recipe to make12 brownies.
3. Each ingredient amount 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. This ratio will be used to adjust the amount of each ingredient.
Ratio=NumberofbrownieswewanttomakeNumberofbrowniestherecipemakesRatio = \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=1216Ratio = \frac{12}{16}

STEP 4

implify the ratio.
Ratio=1216=34Ratio = \frac{12}{16} = \frac{3}{4}

STEP 5

Now that we have the ratio, we can find the amount of each ingredient needed for12 brownies. This can be done by multiplying the amount of each ingredient in the original recipe by the ratio.
Amountfor12brownies=OriginalamounttimesRatioAmount\, for\,12\, brownies = Original\, amount \\times Ratio

STEP 6

Plug in the values for the original amount of butter and the ratio to calculate the amount of butter needed for12 brownies.
Butterfor12brownies=12cuptimes34Butter\, for\,12\, brownies = \frac{1}{2}\, cup \\times \frac{3}{4}

STEP 7

Calculate the amount of butter needed for12 brownies.
Butterfor12brownies=12cuptimes34=3cupButter\, for\,12\, brownies = \frac{1}{2}\, cup \\times \frac{3}{4} = \frac{3}{}\, cupRepeat steps6 and7 for each ingredient to find the amount needed for12 brownies.

STEP 8

For chocolate,
Chocolatefor12brownies=212ouncestimes34Chocolate\, for\,12\, brownies =2 \frac{1}{2}\, ounces \\times \frac{3}{4}

STEP 9

Calculate the amount of chocolate needed for12 brownies.
Chocolatefor12brownies=22ouncestimes34=.875ouncesChocolate\, for\,12\, brownies =2 \frac{}{2}\, ounces \\times \frac{3}{4} =.875\, ounces

STEP 10

For sugar,
Sugarfor12brownies=cuptimes34Sugar\, for\,12\, brownies =\, cup \\times \frac{3}{4}

STEP 11

Calculate the amount of sugar needed for brownies.
Sugarforbrownies=cuptimes34=34cupSugar\, for\,\, brownies =\, cup \\times \frac{3}{4} = \frac{3}{4}\, cup

STEP 12

For vanilla,
Vanillafor12brownies=2teaspoontimes4Vanilla\, for\,12\, brownies = \frac{}{2}\, teaspoon \\times \frac{}{4}

STEP 13

Calculate the amount of vanilla needed for12 brownies.
Vanillafor12brownies=2teaspoontimes3=38teaspoonVanilla\, for\,12\, brownies = \frac{}{2}\, teaspoon \\times \frac{3}{} = \frac{3}{8}\, teaspoon

STEP 14

For eggs,
ggsfor12brownies=2eggstimes34ggs\, for\,12\, brownies =2\, eggs \\times \frac{3}{4}

STEP 15

Calculate the amount of eggs needed for12 brownies.
ggsfor12brownies=2eggstimes34=.5eggsggs\, for\,12\, brownies =2\, eggs \\times \frac{3}{4} =.5\, eggs

STEP 16

For flour,
Flourfor12brownies=34cuptimes34Flour\, for\,12\, brownies = \frac{3}{4}\, cup \\times \frac{3}{4}

STEP 17

Calculate the amount of flour needed for12 brownies.
Flourfor12brownies=34cuptimes34=916cupFlour\, for\,12\, brownies = \frac{3}{4}\, cup \\times \frac{3}{4} = \frac{9}{16}\, cupSo, to make12 brownies, you need 3\frac{3}{} cup of butter,.875 ounces of chocolate, 34\frac{3}{4} cup of sugar, 3\frac{3}{} teaspoon of vanilla,.5 eggs, and 916\frac{9}{16} cup of flour.

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