Question
Sara is making 3 batches of chocolate chip cookies and 3 batches of oatmeal cookies. each batch of chocolate chip cookies uses 2 1/4 cups of flours. she will use 12 3/4 cups of flours for all six batches, determine how many cups of flour are needed for each batch of oatmeal cookies
Answers
Answered by
GPT-4o mini
To determine how many cups of flour are needed for each batch of oatmeal cookies, we first need to calculate the total amount of flour Sara is using for the chocolate chip cookies and then find out how much flour is left for the oatmeal cookies.
1. **Calculate the total flour used for the chocolate chip cookies:**
Each batch of chocolate chip cookies uses \( 2 \frac{1}{4} \) cups of flour. To convert this mixed number to an improper fraction:
\[
2 \frac{1}{4} = \frac{9}{4} \text{ cups}
\]
Since there are 3 batches of chocolate chip cookies, the total flour used for them is:
\[
3 \times \frac{9}{4} = \frac{27}{4} \text{ cups}
\]
2. **Convert the total flour used for the chocolate chip cookies to a decimal or mixed number if necessary:**
\[
\frac{27}{4} = 6 \frac{3}{4} \text{ cups} = 6.75 \text{ cups}
\]
3. **Calculate the total flour used for all cookies:**
Sara will use \( 12 \frac{3}{4} \) cups for all six batches of cookies, which as an improper fraction is:
\[
12 \frac{3}{4} = \frac{51}{4} \text{ cups}
\]
4. **Calculate the flour used for oatmeal cookies:**
Now we subtract the flour used for the chocolate chip cookies from the total flour:
\[
\text{Flour for oatmeal cookies} = \frac{51}{4} - \frac{27}{4} = \frac{51 - 27}{4} = \frac{24}{4} = 6 \text{ cups}
\]
5. **Determine the flour needed for each batch of oatmeal cookies:**
Since there are 3 batches of oatmeal cookies, we divide the total flour for oatmeal cookies by the number of batches:
\[
\text{Flour per batch of oatmeal cookies} = \frac{6}{3} = 2 \text{ cups}
\]
Thus, each batch of oatmeal cookies requires 2 cups of flour.
1. **Calculate the total flour used for the chocolate chip cookies:**
Each batch of chocolate chip cookies uses \( 2 \frac{1}{4} \) cups of flour. To convert this mixed number to an improper fraction:
\[
2 \frac{1}{4} = \frac{9}{4} \text{ cups}
\]
Since there are 3 batches of chocolate chip cookies, the total flour used for them is:
\[
3 \times \frac{9}{4} = \frac{27}{4} \text{ cups}
\]
2. **Convert the total flour used for the chocolate chip cookies to a decimal or mixed number if necessary:**
\[
\frac{27}{4} = 6 \frac{3}{4} \text{ cups} = 6.75 \text{ cups}
\]
3. **Calculate the total flour used for all cookies:**
Sara will use \( 12 \frac{3}{4} \) cups for all six batches of cookies, which as an improper fraction is:
\[
12 \frac{3}{4} = \frac{51}{4} \text{ cups}
\]
4. **Calculate the flour used for oatmeal cookies:**
Now we subtract the flour used for the chocolate chip cookies from the total flour:
\[
\text{Flour for oatmeal cookies} = \frac{51}{4} - \frac{27}{4} = \frac{51 - 27}{4} = \frac{24}{4} = 6 \text{ cups}
\]
5. **Determine the flour needed for each batch of oatmeal cookies:**
Since there are 3 batches of oatmeal cookies, we divide the total flour for oatmeal cookies by the number of batches:
\[
\text{Flour per batch of oatmeal cookies} = \frac{6}{3} = 2 \text{ cups}
\]
Thus, each batch of oatmeal cookies requires 2 cups of flour.