If it takes 2 cups of cocoa and 1 cup of sugar to make nine brownies, how many cups of cocoa and sugar, would it take to make 81 brownies
Since it takes 2 cups of cocoa and 1 cup of sugar to make 9 brownies, we can set up a proportion to find out how many cups of cocoa and sugar it would take to make 81 brownies.
Let x represent the number of cups of cocoa and sugar needed to make 81 brownies.
According to the proportion, we have:
2 cups of cocoa / 1 cup of sugar = 9 brownies / x cups of cocoa and sugar.
Using cross multiplication, we can solve for x:
2 * x = 1 * 81
2x = 81
Now, we can solve for x:
x = 81 / 2.
x = 40.5.
Therefore, it would take 40.5 cups of cocoa and sugar to make 81 brownies.
To find out how many cups of cocoa and sugar are needed to make 81 brownies, we can set up a proportion based on the given information.
According to the given information:
2 cups of cocoa + 1 cup of sugar = 9 brownies
Let's use "x" to represent the number of cups of cocoa and sugar needed to make 81 brownies. The proportion can be set up as:
2 cups of cocoa + 1 cup of sugar = 9 brownies
x cups of cocoa + x/2 cups of sugar = 81 brownies
Now we can set up the cross-products:
2 * 81 = 9 * (x + x/2)
Simplifying this equation:
162 = 9 * (3x/2)
Divide both sides by 9:
162/9 = (3x/2)
18 = (3x/2)
Multiply both sides by 2/3:
18 * (2/3) = (3x/2) * (2/3)
12 = x
Therefore, it would take 12 cups of cocoa and 6 cups of sugar to make 81 brownies.
To find out how many cups of cocoa and sugar are needed to make 81 brownies, we can use a ratio and proportion method.
First, let's calculate the ratio of cocoa to brownies. We know that 2 cups of cocoa are needed to make 9 brownies. Thus, the ratio of cocoa to brownies can be expressed as 2/9.
Next, we need to find the ratio of sugar to brownies. Given that 1 cup of sugar is used to make 9 brownies, the ratio of sugar to brownies is 1/9.
Now, since we want to know how much cocoa and sugar are required for 81 brownies, we can set up a proportion.
Let "x" represent the amount of cocoa needed, and "y" represent the amount of sugar needed.
The ratio of cocoa to sugar in the recipe is the same as the ratio of cocoa to sugar in the proportion, which is 2/1 (cocoa to sugar):
2/1 = x/y
To solve for x and y, we can cross-multiply:
2y = x
Now we can plug this into the first ratio of cocoa to brownies (2/9):
2y/9 = x/81
Next, we can solve for y by multiplying both sides of the equation by 9:
2y = (x/81) * 9
2y = x/9
Now we can substitute the value of x from the previous equation into our equation for y:
2y = (2y/9)/9
Simplifying further:
2y = 2y/81
To find the value of y, we can cross-multiply:
2y * 81 = 2y
162y = 2y
Subtracting 2y from both sides:
162y - 2y = 0
160y = 0
Dividing both sides of the equation by 160:
y = 0
This means that no cups of sugar are needed to make 81 brownies. However, it is possible that this is an error or omission in the question, as it is highly unlikely that no sugar would be required in a brownie recipe.