One packet of biscuits requires `2(1/2)` cups of flour and `1(2/3)` cups of sugar. Estimated total quantity of both ingredients used in 10 such packets of biscuits will be:

Options

A. less than 30 cups
B. between 30 cups and 40 cups
C. between 40 cups and 50 cups
D. above 50 cups

Answer

To solve the problem step by step, we need to calculate the total quantity of flour and sugar required for 10 packets of biscuits.

### Step 1: Convert Mixed Numbers to Improper Fractions
1. **Flour:** The requirement for one packet of biscuits is `2(1/2)` cups of flour.
- Convert `2(1/2)` to an improper fraction:
\[ 2(1/2) = 2 \times 2 + 1 = 4 + 1 = \frac{5}{2} \]

2. **Sugar:** The requirement for one packet of biscuits is `1(2/3)` cups of sugar.
- Convert `1(2/3)` to an improper fraction:
\[ 1(2/3) = 1 \times 3 + 2 = 3 + 2 = \frac{5}{3} \]

### Step 2: Find Total Ingredients for One Packet
Now, we need to find the total quantity of flour and sugar for one packet:
\[ \text{Total for one packet} = \frac{5}{2} + \frac{5}{3} \]

### Step 3: Find a Common Denominator
To add these fractions, we need a common denominator. The denominators are 2 and 3. The least common multiple (LCM) of 2 and 3 is 6.

### Step 4: Convert Fractions to Have the Same Denominator
Convert both fractions to have a denominator of 6:
- For \(\frac{5}{2}\):
\[ \frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6} \]
- For \(\frac{5}{3}\):
\[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]

### Step 5: Add the Fractions
Now we can add the two fractions:
\[ \frac{15}{6} + \frac{10}{6} = \frac{15 + 10}{6} = \frac{25}{6} \]

### Step 6: Calculate Total for 10 Packets
Now, we need to find the total quantity of ingredients for 10 packets:
\[ \text{Total for 10 packets} = 10 \times \frac{25}{6} = \frac{250}{6} \]

### Step 7: Simplify the Fraction
To simplify \(\frac{250}{6}\):
\[ \frac{250}{6} = \frac{125}{3} \]

### Step 8: Convert to Mixed Number
Now, we can convert \(\frac{125}{3}\) to a mixed number:
- Divide 125 by 3:
- 3 goes into 125, 41 times (since \(3 \times 41 = 123\)).
- The remainder is \(125 - 123 = 2\).

Thus, \(\frac{125}{3} = 41 \frac{2}{3}\).

### Final Answer
The estimated total quantity of both ingredients used in 10 packets of biscuits will be:
\[ 41 \frac{2}{3} \text{ cups} \]

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