A baker is using a cookie recipe that call for 2 ¼ cups of flour to yield 36 cookies. How much flour will the baker need to make 90 cookies using the same recipe?
A.
6 ¾ cups
B.
5 5/8 cups
C.
10 1/8 cups
D.
4 ¾ cups
The Correct Answer and Explanation is:
To determine how much flour is needed to make 90 cookies using the same recipe, we need to scale up the flour amount proportionally from the original recipe. The original recipe yields 36 cookies with 2 ¼ cups of flour.
Here’s a step-by-step approach to solve this problem:
- Determine the flour required for one cookie:The recipe calls for 2 ¼ cups of flour to make 36 cookies. First, convert 2 ¼ cups to an improper fraction:214=94 cups2 \frac{1}{4} = \frac{9}{4} \text{ cups}241=49 cupsTo find the flour needed for one cookie, divide the total flour by the number of cookies:94÷36=94×136=9144=116 cups per cookie\frac{9}{4} \div 36 = \frac{9}{4} \times \frac{1}{36} = \frac{9}{144} = \frac{1}{16} \text{ cups per cookie}49÷36=49×361=1449=161 cups per cookie
- Calculate the flour needed for 90 cookies:To find out how much flour is required for 90 cookies, multiply the amount of flour needed per cookie by 90:116×90=9016=51016=558 cups\frac{1}{16} \times 90 = \frac{90}{16} = 5 \frac{10}{16} = 5 \frac{5}{8} \text{ cups}161×90=1690=51610=585 cupsTherefore, the baker needs 5 5/8 cups of flour to make 90 cookies.
- Verify the answer:For further verification, use a proportional approach. If 2 ¼ cups of flour yield 36 cookies, to find the amount of flour required for 90 cookies, set up a proportion:21436=x90\frac{2 \frac{1}{4}}{36} = \frac{x}{90}36241=90xSolve for xxx:94×9036=9×904×36=810144=558\frac{9}{4} \times \frac{90}{36} = \frac{9 \times 90}{4 \times 36} = \frac{810}{144} = 5 \frac{5}{8}49×3690=4×369×90=144810=585
Thus, the correct answer is:
B. 5 5/8 cups