Question

A baker is using a cookie that calls for 2 1/4 cups of flour to yield 36 cookies, how much flour will the baker neeto to make 90 cookies using the same recddipe?

Answer 1

The answer involves creating a proportion based on the recipe's original yield of 36 cookies with 2 1/4 cups of flour to find out how much flour is needed to make 90 cookies. The solution reveals that 5.625 cups of flour are required.

Step-by-step explanation:

The student wants to know how much flour is required to scale up a cookie recipe. The original recipe calls for 2 1/4 cups of flour to make 36 cookies. To find out how much flour is needed for 90 cookies, we can set up a proportion since the number of cookies increases by a factor. First, we convert 2 1/4 cups to a decimal which is 2.25 cups of flour. Then we set up our proportion comparing the original amount of flour to the original number of cookies, and the unknown amount of flour to the new number of cookies.

The proportion looks like this: 2.25 cups of flour/36 cookies = x cups of flour/90 cookies. By cross-multiplying and solving for x, we get x = (2.25 * 90) / 36. The calculation yields x = 5.625 cups of flour needed for 90 cookies.

Answer 2

`5 (5)/(8)` cups

Step-by-step explanation:

Given: A baker is using a cookie that calls for 2
`(1)/(4)` cups of flour to yield 36 cookies.

To find the number of flour will the baker need to make 90 cookies, we form a proportion.

Let's convert 2
`(1)/(4)` to improper fraction.

`2(1)/(4) = ((2*4) + 1)/(4) = (9)/(4)`

Let "x" be the amount flour to make 90 cookies

Amount of Flour Number of cookies

`(9)/(4)` 36

x 90

Now form a proportion.

`((9)/(4))/(x) = (36)/(90)`

Now let's cross multiply, we get

`(9)/(4) *90 = 36x\\\`

`(810)/(4) = 36x\\x = (810 )/(4*36) \\x = (810)/(144) \\\\x = 5 (90)/(144)`

Now let's simplify the fraction part, Here the GCF of 90 and 144 is 18, so dividing the fraction's numerator and the denominator by 18, we get

x =
`5 (5)/(8)` cups

So the baker needs
`5 (5)/(8)` cups to make 90 cookies.