The bakery chef at Central Supermarket is collecting the ingredients to bake some brownies. His cookbook contains this ingredient list:
INGREDIENTS FOR BROWNIES
1/2 cup butter
1.5 ounces unsweetened chocolate
1 cup sugar
2 eggs
1 teaspoon vanilla
3/4 cup all-purpose flour
1/3 cup chopped nuts
Use a 6-inch by 9-inch baking pan.
However, the chef needs to use a commercial-size baking pan, 18 inches by 2 feet.
Figure out how much of each ingredient would be needed to bake brownies in this pan. Explain how you found your answer and how you know it is correct.
(The brownies should still have the same thickness as in the original recipe.)
1. The answers for this post were kind of all over the place. A couple of things you should have been thinking about as you solved this problem:
2. Did you include the units? Were you suppose to use cups, teaspoons? This would have a huge effect on the new batch of brownies.
3. Did you fractions make sense? Could a larger recipe call for less of an ingredient?
4. How many dimensions are you enlarging? This problem call for you to use the area of the pan, (we didn't even have to think about the volume - whew!) which is two dimensions. Because you were using two dimensions we need to take that scale factor for both sides and multiply them together or as we learned in the scaling project to square our scale factor.
Make sure to slow down and think about the POW if it seems so obvious you may want to re-read the problem to be sure you have all the information you need to solve the problem.
Ms. L.
The correct answer:
The new recipe
4 cups butter
12 ounces unsweetened chocolate
8 cups sugar
16 eggs
8 teaspoons vanilla
6 cups all-purpose flour
8/3 cups chopped nuts
1. The answers for this post were kind of all over the place. A couple of things you should have been thinking about as you solved this problem:
2. Did you include the units? Were you suppose to use cups, teaspoons? This would have a huge effect on the new batch of brownies.
3. Did you fractions make sense? Could a larger recipe call for less of an ingredient?
4. How many dimensions are you enlarging? This problem call for you to use the area of the pan, (we didn't even have to think about the volume - whew!) which is two dimensions. Because you were using two dimensions we need to take that scale factor for both sides and multiply them together or as we learned in the scaling project to square our scale factor.
Make sure to slow down and think about the POW if it seems so obvious you may want to re-read the problem to be sure you have all the information you need to solve the problem.
Ms. L.
The correct answer:
The new recipe
4 cups butter
12 ounces unsweetened chocolate
8 cups sugar
16 eggs
8 teaspoons vanilla
6 cups all-purpose flour
8/3 cups chopped nuts
19 comments:
SK
SF 5.8
Butter: 2.9cups
Unsweetened Chocolate: 8.7 Ounces
Sugar: 5.8 cups
Eggs: 12
Vanilla: 5.8 Teaspoons
All purpose flour: 4.35 cups
Chopped Nuts: 1.914 cups
What I did to get my answer was truly simple. All you had to do is discover the scale factor between the pans, and then apply the same scale factor to each and every other ingredient. To get the scale factor, I multiplied the side lengths by two, then added the side lengths of each pan with the other side length on the same pan, then divided the larger number by the smaller one, and then I had my scale factor being 5.8. After applying the same scale factor to each ingredient, I had my result.
BV
SF 5.8
Butter: 2.9cups
Unsweetened Chocolate: 8.7 Ounces
Sugar: 5.8 cups
Eggs: 12
Vanilla: 5.8 Teaspoons
All purpose flour: 4.35 cups
Chopped Nuts: 1.914 cups
All you had to do is discover the scale factor between the pans, and then apply the same scale factor to each and every other ingredient. To get the scale factor, I multiplied the side lengths by two, then added the side lengths of each pan with the other side length on the same pan, then divided the larger number by the smaller one, and then I had my scale factor being 5.8. After applying the same scale factor to each ingredient, I had my result.
AM
This problem you need to multiply all the ingredients by two. You do that because (6/9), x (18/24) =.5 and .5x2=1
1 cup butter
3 ounces unsweetened chocolate
2 cup sugar
4 eggs
2 teaspoon vanilla
1 1/2 cup all-purpose flour
2/3 cup chopped nuts
MJS
SF:2.9
Butter:1.45
Unsweetened chocolate:4.35
Cup sugar:5.8
Eggs:6
Teaspoon Vanilla:2.9
4.35: All purpose sugar
1.914: Chopped nuts.
I got this answer by multiplying the pan by the highest thing. That wouldn’t make anything way bigger than everything else. The 2.9 is the only thing that wouldn’t make the pan way over.
RT
3/9 cup butter
6.75 ounces unsweetened chocolate
4.5 cup sugar
9 eggs
4.5 teaspoon vanilla
9/18 cup all-purpose flour
3/13.5 cup chopped nuts
I got these answers by figuring out that 6 goes into 18 3 times and 4.5 goes into 9 2 times. So for each ingredient I multiplied the first number by 3 and for the second number I multiplied it by 4.5. But for each whole number I just multiplied 4.5 by the whole number. That’s how I got my answers for the ingredients.
J.M.
I multiplied 6 by 3 to get 18 and I multiplied 9 by 2.6 to get around 24. Then I multiplied all of the ingredients by 3. I know it is correct because I checked my work twice.
CB
Butter: 3/9 cups
Unsweetened chocolate: 6.75 ounces
Sugar: 4.5 cups
Eggs: 9
Teaspoons of vanilla: 4.5 tsp.
Flour: 9/18 cups
Nuts: 13.5 cups
I found my answer in a multitude of ways. First off I created a new fraction for the ingredients. I found that 6 goes into 18 3 times, and 2 goes into 9 4.5 times, thus I had my fraction. For the butter it was simple multiplication, but for the others, it required different methods. I multiplied the whole numbers by my whole number, 4.5. As I multiplied the old numbers, I plugged them in to my new slots.
TD
Reciepe
Butter-3/9
Chocolate-6.75 ounces
Sugar- 4.5 cups
Eggs-9
Vanilla-4.5 tsp
Flour-9/18 cup
Nuts- 13.5 cups
I found my answer with many different steps. First I had to find a scale factor to get from the smaller to the larger. I figured out, that 18 divided by 3 is 6 and 2 goes into 94 5 times. So then I had my scale factor, 4.5. for the butter I multiplied 3/9 by 3/5.5 to get 3/9. for the chocolate I multiplied to get 6.75 and so forth. For the rest I only multiplied by whole number. I multiplied what ever the original number was, by my number, 4.5.
BV
SF 2.9
Butter: 2.9cups
Unsweetened Chocolate: 4.35 Ounces
Sugar: 2.9 cups
Eggs: 6
Vanilla: 2.9 Teaspoons
All purpose flour: 2.175 cups
Chopped Nuts: .957 cups
All you had to do is discover the scale factor between the pans, and then apply the same scale factor to each and every other ingredient. To get the scale factor, I multiplied the side lengths by two, then added the side lengths of each pan with the other side length on the same pan, then divided the larger number by the smaller one, and then I had my scale factor being 2.9. After applying the same scale factor to each ingredient, I had my result.
WO
The brownies do not have to fit into the pan. They only have to be the same thickness.
1 cup butter
3 ounces unsweetened chocolate
2 cup sugar
4 eggs
2 teaspoon vanilla
1 2/4 cup all-purpose flour
2/3 cup chopped nuts
HW
For this problem, you have to multiply all of the ingredients by eight, because 6x9=54, and 18x24 = 432, and 432/54=8.
4 cup butter
12 ounces unsweetened chocolate
8 cup sugar
16 eggs
8 teaspoon vanilla
6 cup all-purpose flour
2 2/3 cup chopped nuts
A.L.
INGREDIENTS
1 ½ cups of butter
4.5 ounces of unsweetened chocolate
3 cups of sugar
6 eggs
3 teaspoons of vanilla
2 ¼ cups of all – purpose flour
1 cup of chopped nuts
How I got this is by dividing 24 by 3 to get 8. I did that for every number and found out their all divisible by 3. So I got my scale factor from there to get; for every ingredient, you need to multiply it by 3. So that is how I got my answer (s).
EEW
The scale factor is 3.
1.5 cups of butter
4.5 ounces of chocolate
3 cups of sugar
6 eggs
3 teaspoons of vanilla
2 ¼ cups of flour
1 cup of chopped nuts
I figured this out bt dividing the size of the pans, and got 3. then I multiplied the ingredients by that.
BT
The scale factor is 8. I figured this out by finding the area for each pan. The area for the first pan was 54 inches. The area for the enlarged pan was 432 inches. If you divide 432 by 54, you get 8.
4 cups of butter
12 ounces of unsweetened chocolate
8 cups of sugar
16 eggs
8 teaspoons of vanilla
6 cups of all-purpose flour
2.64 cups of chopped nuts
I found these out by multiplying the original amounts by 8.
ZB
The ingredient measurement should be about 8 times as much as the original amount. I found the area of the original figure (54) and the area of the larger one (432). I divided 432 by 54 and I got 8. All the measurements would be multiplied by 8 to get the new recipe measurements.
4 cups of butter
12 ounces of unsweetened chocolate
8 cups of sugar
16 eggs
8 teaspoons of vanilla
6 cups off all purpose flour
3 cups of chopped nuts
MW
The ingredients will each need to be multiplied by 8. I came to this conclusion because I looked at the areas. So you would multiply 6 by 9, which is 54, and 18 by 24, which is 432, and the scale factor is 8. Which means that everything including the area would need to be multiplied by 8.
AR
4.5 cups butter
13.5 ounces unsweetened chocolate
9 cups sugar
18 eggs
9 teaspoons vanilla
6.75 cups all- purpose flour
3 cups chopped nuts
To solve this you must find the scale factor from the original area to the new area. To do this, find the scale factor of the side lengths. That is 2.8 so round it to 3. Multiply 3 times 3. Then multiply that (9) by each ingredient.
TM
4 cups of butter
12 ounces of unsweetened chocolate
8 cups of sugar
16 eggs
8 teaspoons of vanilla
6 cups of all purpose flour
2.64 cups of chopped nuts
I got these by figuring out the square inches in each pan, in the smaller one there are 54 square inches and in the big one there are 432 square inches. If you divide the two numbers you get eight and that what I used to multiply all of the ingredients to get the new ones.
A.W.
In order to get the answer for this problem, you need to find a scale factor. You can do that by finding all the areas for both of the pans. For the first pan, the area is 54 inches. I got that by multiplying 6 by 9, and that equaled 54. For the second pan, the area would be 432 inches. I got this one by multiplying 24 by 18. The scale factor for both of the areas would be 8. So you have to multiply each ingredient by 8.
NEW INGREDIENTS FOR BROWNIES:
4 cups of butter
12 ounces of unsweetened chocolate
8 cups of sugar
16 eggs
8 teaspoons of vanilla
6cups of all-purpose flour
2 cups of chopped nuts
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