Sara is making cookies and the recipe calls for 2 1/2 (2.5) cups of sugar to make two dozen cookies. How many cups of sugar will she need to make five dozen cookies? Express the answer as a mixed fraction and as a decimal
Cross multiply the proportion and solve for x.
2.5/24 = x/ 60
To find out how many cups of sugar Sara will need to make five dozen cookies, we can set up a proportion equation using the given information.
Let's start by setting up the proportion:
2.5 cups of sugar = 2 dozen cookies
To find the amount of sugar needed for 5 dozen cookies, we can set up the proportion like this:
2.5 cups of sugar / 2 dozen cookies = x cups of sugar / 5 dozen cookies
First, let's convert 5 dozen cookies into the actual number of cookies.
5 dozen cookies = 5 x 12 = 60 cookies
Now let's solve the proportion equation to find x, the number of cups of sugar needed for 5 dozen cookies:
2.5 cups of sugar / 2 dozen cookies = x cups of sugar / 60 cookies
Now let's cross multiply:
2.5 cups of sugar * 60 cookies = 2 dozen cookies * x cups of sugar
150 cups of sugar = 2x
Divide both sides by 2 to solve for x:
150 cups of sugar / 2 = 2x / 2
75 cups of sugar = x
So, Sara will need 75 cups of sugar to make five dozen cookies.
To express the answer as a mixed fraction, we divide the total cups of sugar (75) by the number of cups in one dozen (12):
75 cups of sugar / 12 = 6 remainder 3
So the mixed fraction is 6 and 3/12 cups of sugar.
To express the answer as a decimal, we divide the total cups of sugar (75) by the number of cups in one dozen (12):
75 cups of sugar ÷ 12 = 6.25
Therefore, Sara will need 6 and 3/12 cups of sugar or 6.25 cups of sugar to make five dozen cookies.
To find out how many cups of sugar Sara will need to make five dozen cookies, we first need to determine the relationship between the number of cookies and the amount of sugar required.
Given that 2.5 cups of sugar are needed for 2 dozen cookies, we can set up a proportion to find the amount of sugar needed for 5 dozen cookies.
Let's set up the proportion:
2.5 cups of sugar / 2 dozen cookies = x cups of sugar / 5 dozen cookies
To solve for x, we cross multiply:
2.5 cups of sugar * 5 dozen cookies = 2 dozen cookies * x cups of sugar
12.5 cups of sugar = 24 cookies * x cups of sugar
Now, we can solve for x by dividing both sides of the equation by 24 cookies:
12.5 cups of sugar / 24 cookies = x cups of sugar
To express the answer as a mixed fraction, we divide:
12.5 / 24 ≈ 0.52
To convert the decimal to a mixed fraction, we multiply it by the reciprocal of 1/24, which is 24/1. This gives us:
0.52 * (24/1) = 12.48/1
Now, we express it as a mixed fraction by dividing the numerator by the denominator:
12.48 ÷ 1 = 12 whole cups + 48/1 cups = 12 48/1 cups
Therefore, Sara will need approximately 12 48/1 cups of sugar to make five dozen cookies.