1 batch . . . . 2-1/4 cups
2 batches . . 4-1/2 cups
3 batches . . 6-3/4 cups
4 batches . . 9 cups
.
.
7 batches . . 7(2 + 1/4) =
(7 x 2) + (7 x 1/4) =
14 + ( 7/4) =
14 + 1-3/4 = 15-3/4
c). Write a proportion: (1 batch) /(3 dozen) = (x) / (200 cookies)
1 dozen = 12 cookies
3 dozen = 36 cookies
So the proportion is (1 batch)/(36 cookies) = (x) / (200 cookies)
Cross-multiply: (1 batch) x (200 cookies) = ('x' batch) x (36 cookies)
Divide each side by (36 cookies):
(1 batch x 200 cookies / 36 cookies) = 'x' batch
(200 batch / 36) = 'x' batch
x = 200/36 = 5.55 batches
If you can only make whole batches, then you need to make 6 of them
in order to have at least 200 cookies.
d). There's more than one possible unit rate here:
-- 2.25 cup flour per batch
-- 0.75 cup flour per dozen cookies
-- 0.0625 cup flour per cookie
-- 16 cookies per cup flour
-- 0.444 batch per cup flour
etc.