Question

1. betty crocker spent most of her adulthood using measurements to perfect her recipes in her standard cake recipe, she uses 2 cups of water for every 3 cups of flour. she has more people coming over so that she now needs 8 cups of flour. how many cups of water will she require?

a. $3\frac{2}{3}$
b. 4
c. $5\frac{1}{3}$
d. 6

Explanation:

Step1: Set up the proportion

Let \( x \) be the number of cups of water needed. The ratio of water to flour in the original recipe is \( \frac{2}{3} \), and in the new recipe, it is \( \frac{x}{8} \). Since the ratio should be the same, we set up the proportion:
\( \frac{2}{3} = \frac{x}{8} \)

Step2: Solve for \( x \)

Cross - multiply: \( 3x = 2\times8 \)
\( 3x = 16 \)
Then, \( x=\frac{16}{3}=5\frac{1}{3} \)? Wait, no, wait. Wait, original ratio: 2 cups water for 3 cups flour. Now flour is 8 cups. Wait, maybe I made a mistake. Wait, let's re - examine.

Wait, the original ratio is water (W) to flour (F): \( W:F = 2:3 \). Now, F = 8. We need to find W.

So, using the proportion \( \frac{W_1}{F_1}=\frac{W_2}{F_2} \), where \( W_1 = 2 \), \( F_1 = 3 \), \( F_2 = 8 \), \( W_2=x \).

So \( \frac{2}{3}=\frac{x}{8} \), cross - multiply: \( 3x=2\times8 = 16 \), \( x=\frac{16}{3}=5\frac{1}{3} \)? But wait, the options have \( 5\frac{1}{3} \) as option c. Wait, but let's check again.

Wait, maybe the original ratio is 2 cups water for 3 cups flour. So the rate of water per cup of flour is \( \frac{2}{3} \) cups of water per cup of flour.

Now, for 8 cups of flour, the water needed is \( 8\times\frac{2}{3}=\frac{16}{3}=5\frac{1}{3} \) cups.

Answer:

c. \( 5\frac{1}{3} \)