Sujay eats `2 (2)/(3)` packets of cookies in a day. How many packets of cookies will he eat in `17 (1)/(2)` days?

Options

A. `= 86 (2)/(3)`
B. `= 46 (2)/(9)`
C. `= 49 (2)/(3)`
D. `= 46 (2)/(3)`

Answer

To solve the problem of how many packets of cookies Sujay will eat in `17 (1)/(2)` days, we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. **Convert `2 (2)/(3)` to an improper fraction:**
- Multiply the whole number (2) by the denominator (3):
\(2 \times 3 = 6\)
- Add the numerator (2) to this result:
\(6 + 2 = 8\)
- So, \(2 (2)/(3) = \frac{8}{3}\).

2. **Convert `17 (1)/(2)` to an improper fraction:**
- Multiply the whole number (17) by the denominator (2):
\(17 \times 2 = 34\)
- Add the numerator (1) to this result:
\(34 + 1 = 35\)
- So, \(17 (1)/(2) = \frac{35}{2}\).

### Step 2: Multiply the Fractions
Now, we will multiply the number of packets Sujay eats in one day by the number of days.

\[ \text{Total packets} = \left(\frac{8}{3}\right) \times \left(\frac{35}{2}\right) \]

### Step 3: Perform the Multiplication
Multiply the numerators and the denominators:

\[ \text{Numerator: } 8 \times 35 = 280 \]
\[ \text{Denominator: } 3 \times 2 = 6 \]

So, we have:

\[ \text{Total packets} = \frac{280}{6} \]

### Step 4: Simplify the Fraction
Now, we simplify \(\frac{280}{6}\):

- Find the greatest common divisor (GCD) of 280 and 6, which is 2.
- Divide both the numerator and the denominator by 2:

\[ \frac{280 \div 2}{6 \div 2} = \frac{140}{3} \]

### Step 5: Convert to Mixed Number
Now, we convert \(\frac{140}{3}\) to a mixed number:

1. Divide 140 by 3:
- \(140 \div 3 = 46\) remainder \(2\).
2. So, \(\frac{140}{3} = 46 \frac{2}{3}\).

### Final Answer
Sujay will eat \(46 \frac{2}{3}\) packets of cookies in \(17 (1)/(2)\) days.

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