`5(1/4)` kg of oranges and `2(3/5)`kg of grapes were bought together by Alisha from the supermarket. What is the total weight of the fruits will she be carrying out of supermarket ?

Options

A. `8(5/13)` kg
B. `7(17/20)` kg
C. `7(17/21)` kg
D. `8(9/13)` kg

Answer

To find the total weight of fruits Alisha bought, we need to add the weight of the oranges and the weight of the grapes. Let's break it down step by step.

### Step 1: Convert the mixed numbers to improper fractions
1. **Weight of Oranges**: \(5 \frac{1}{4}\) kg
- Convert to an improper fraction:
\[ 5 \frac{1}{4} = \frac{(5 \times 4) + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} \text{ kg} \]

2. **Weight of Grapes**: \(2 \frac{3}{5}\) kg
- Convert to an improper fraction:
\[ 2 \frac{3}{5} = \frac{(2 \times 5) + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5} \text{ kg} \]

### Step 2: Find a common denominator
To add the two fractions \(\frac{21}{4}\) and \(\frac{13}{5}\), we need a common denominator. The least common multiple (LCM) of 4 and 5 is 20.

### Step 3: Convert the fractions to have the common denominator
1. Convert \(\frac{21}{4}\):
\[ \frac{21}{4} = \frac{21 \times 5}{4 \times 5} = \frac{105}{20} \]

2. Convert \(\frac{13}{5}\):
\[ \frac{13}{5} = \frac{13 \times 4}{5 \times 4} = \frac{52}{20} \]

### Step 4: Add the two fractions
Now we can add the two fractions:
\[ \frac{105}{20} + \frac{52}{20} = \frac{105 + 52}{20} = \frac{157}{20} \]

### Step 5: Convert the improper fraction to a mixed number
To convert \(\frac{157}{20}\) to a mixed number:
- Divide 157 by 20:
- 20 goes into 157 seven times (since \(20 \times 7 = 140\)).
- The remainder is \(157 - 140 = 17\).

Thus, we can write:
\[ \frac{157}{20} = 7 \frac{17}{20} \text{ kg} \]

### Final Answer
The total weight of the fruits Alisha will be carrying out of the supermarket is \(7 \frac{17}{20}\) kg.

---