To find out how much oats Karen started with, let's break down the usage and the remaining oats step-by-step:
1. Oats used in the meatloaf:
- Karen used [tex]\(1 \frac{1}{4}\)[/tex] cups of oats in the meatloaf. Converting the mixed number to an improper fraction, we get:
[tex]\[
1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \text{ cups.}
\][/tex]
- Converting this to a decimal for easier calculation:
[tex]\[
\frac{5}{4} = 1.25 \text{ cups.}
\][/tex]
2. Oats used in the cookies:
- Karen used [tex]\(3 \frac{1}{4}\)[/tex] cups of oats in the cookies. Converting the mixed number to an improper fraction, we get:
[tex]\[
3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4} \text{ cups.}
\][/tex]
- Converting this to a decimal:
[tex]\[
\frac{13}{4} = 3.25 \text{ cups.}
\][/tex]
3. Oats used in the granola:
- Karen used twice the amount of oats she used to make cookies. Since she used [tex]\(3.25\)[/tex] cups for cookies, she used:
[tex]\[
2 \times 3.25 = 6.5 \text{ cups of oats for the granola.}
\][/tex]
4. Total oats used:
- Now, we sum up the oats used in the meatloaf, cookies, and granola:
[tex]\[
1.25 \text{ cups (meatloaf)} + 3.25 \text{ cups (cookies)} + 6.5 \text{ cups (granola)} = 11.0 \text{ cups.}
\][/tex]
5. Oats left over:
- Karen had 4 cups of oats left over.
6. Initial amount of oats:
- The initial amount of oats Karen had is the total amount used plus the amount left over:
[tex]\[
\text{Initial amount} = 11.0 \text{ cups (used)} + 4 \text{ cups (left over)} = 15 cups.
\][/tex]
So, Karen started with 15 cups of oats.
