Anuja is baking cookies for her slumber party this weekend. She has one super size package of Sugar Sprinkles and one super size package of Chocolate Turtles. Both packages had to be mixed with flour, brown sugar, and water.
The Sugar Sprinkles package contained of a cup of mix that needs to be mixed with cups of flour, cups of brown sugar, and cups of water. The directions indicate to use 0.1125 of a cup of dough to make one cookie and 1 batch should make a total of
Sugar Sprinkles cookies.
The Chocolate Turtle package contained 0.875 of a cup of mix that needs to be mixed with 3.25 cups of flour, 2.5 cups of brown sugar, and 3.75 cups of water. The directions indicate to use of a cup of dough to make one cookie and 1 batch should make a total of
Chocolate Turtle cookies.
The difference in the number of cookies of each type is
.
To find the difference in the number of cookies of each type, we need to subtract the number of Sugar Sprinkles cookies from the number of Chocolate Turtle cookies.
Let's start by determining the number of Sugar Sprinkles cookies:
The Sugar Sprinkles package contains of a cup of mix, which is used to make one cookie.
So, the number of Sugar Sprinkles cookies can be calculated by dividing the total amount of mix by the amount of mix required for one cookie:
Number of Sugar Sprinkles cookies = Total amount of mix / Amount of mix per cookie
Given that 1 batch of Sugar Sprinkles cookies requires 0.1125 cups of dough and makes a total of Sugar Sprinkles cookies, we can set up the equation:
Sugar Sprinkles cookies = (0.1125 * Total amount of mix) / 0.1125
Next, let's determine the number of Chocolate Turtle cookies:
Similarly, the Chocolate Turtle package contains 0.875 cups of mix, which is used to make one cookie. So, the number of Chocolate Turtle cookies can be calculated as:
Number of Chocolate Turtle cookies = Total amount of mix / Amount of mix per cookie
Given that 1 batch of Chocolate Turtle cookies requires cups of dough and makes a total of Chocolate Turtle cookies, we can set up the equation:
Chocolate Turtle cookies = ( * Total amount of mix) /
Finally, we can find the difference in the number of cookies of each type by subtracting the number of Sugar Sprinkles cookies from the number of Chocolate Turtle cookies:
Difference = Chocolate Turtle cookies - Sugar Sprinkles cookies
Plug in the given values for Total amount of mix, , , , , , , and to calculate the difference.
To calculate the difference in the number of cookies of each type, we first need to find out how many cookies can be made from each package.
For the Sugar Sprinkles package:
- The package contains 1/4 cup of mix.
- To make one cookie, we need 0.1125 cups of dough.
- Therefore, the number of cookies that can be made from this package is:
(1/4) / 0.1125 = 2.222 cookies (approximated to 3 cookies).
For the Chocolate Turtle package:
- The package contains 0.875 cups of mix.
- To make one cookie, we need 0.25 cups of dough.
- Therefore, the number of cookies that can be made from this package is:
0.875 / 0.25 = 3.5 cookies.
Now, to find the difference in the number of cookies:
Sugar Sprinkles cookies - Chocolate Turtle cookies = 3 cookies - 3.5 cookies = -0.5 cookies
Since we cannot have a negative number of cookies, the difference in the number of cookies of each type is 0.