Math

QuestionAdjust the brownie recipe for 12 servings from 16. Calculate the new amounts for each ingredient.

Studdy Solution

STEP 1

Assumptions1. The original recipe makes16 servings. . The quantities of the ingredients are proportional to the number of servings.
3. We need to adjust the recipe to make12 servings.

STEP 2

First, we need to find the ratio of the new number of servings to the original number of servings. This ratio will be used to adjust the quantities of each ingredient.
Ratio=NewnumberofservingsOriginalnumberofservingsRatio = \frac{New\, number\, of\, servings}{Original\, number\, of\, servings}

STEP 3

Now, plug in the given values for the new number of servings and the original number of servings 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 new quantity for each ingredient by multiplying the original quantity by the ratio.
For butterNewquantityofbutter=OriginalquantityofbuttertimesRatioNew\, quantity\, of\, butter = Original\, quantity\, of\, butter \\times Ratio

STEP 6

Plug in the values for the original quantity of butter and the ratio to calculate the new quantity of butter.
Newquantityofbutter=12times34New\, quantity\, of\, butter = \frac{1}{2} \\times \frac{3}{4}

STEP 7

Calculate the new quantity of butter.
Newquantityofbutter=12times34=3cupNew\, quantity\, of\, butter = \frac{1}{2} \\times \frac{3}{4} = \frac{3}{}\, cupRepeat steps5 to7 for each ingredient.

STEP 8

For unsweetened chocolateNewquantityofchocolate=OriginalquantityofchocolatetimesRatioNew\, quantity\, of\, chocolate = Original\, quantity\, of\, chocolate \\times RatioNewquantityofchocolate=212times34=178ouncesNew\, quantity\, of\, chocolate =2\frac{1}{2} \\times \frac{3}{4} =1\frac{7}{8}\, ounces

STEP 9

For sugarNewquantityofsugar=OriginalquantityofsugartimesRatioNew\, quantity\, of\, sugar = Original\, quantity\, of\, sugar \\times RatioNewquantityofsugar=5times34=334cupsNew\, quantity\, of\, sugar =5 \\times \frac{3}{4} =3\frac{3}{4}\, cups

STEP 10

For vanillaNewquantityofvanilla=OriginalquantityofvanillatimesRatioNew\, quantity\, of\, vanilla = Original\, quantity\, of\, vanilla \\times RatioNewquantityofvanilla=2times34=38teaspoonNew\, quantity\, of\, vanilla = \frac{}{2} \\times \frac{3}{4} = \frac{3}{8}\, teaspoon

STEP 11

For eggsNewquantityofeggs=OriginalquantityofeggstimesRatioNew\, quantity\, of\, eggs = Original\, quantity\, of\, eggs \\times RatioNewquantityofeggs=times34=eggsNew\, quantity\, of\, eggs = \\times \frac{3}{4} =\frac{}{}\, eggs

STEP 12

For flourNewquantityofflour=OriginalquantityofflourtimesRatioNew\, quantity\, of\, flour = Original\, quantity\, of\, flour \\times RatioNewquantityofflour=4times4=916cupNew\, quantity\, of\, flour = \frac{}{4} \\times \frac{}{4} = \frac{9}{16}\, cupThe adjusted recipe for12 servings requires- 8\frac{}{8} cup butter- 78\frac{7}{8} ounces unsweetened chocolate- 4\frac{}{4} cups sugar- 8\frac{}{8} teaspoon vanilla- 2\frac{}{2} eggs- 916\frac{9}{16} cup flour

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