A company bought 45 laptops and 15 printers to modernize billing operations. If the price of each laptop was `5/3` times the price of each printer, then what percent of the total cost of the purchase was the total cost of laptops?

Options

A. `72.5%`
B. `78%`
C. `90%`
D. None of these

Answer

To solve the problem step by step, let's define the variables and calculate the required percentage.

### Step 1: Define Variables
Let the price of each printer be \( P \).
Then, the price of each laptop is \( \frac{5}{3}P \).

### Step 2: Calculate Total Cost of Laptops
The company bought 45 laptops, so the total cost of laptops is:
\[ \text{Total Cost of Laptops} = 45 \times \frac{5}{3}P = 75P \]

### Step 3: Calculate Total Cost of Printers
The company bought 15 printers, so the total cost of printers is:
\[ \text{Total Cost of Printers} = 15 \times P = 15P \]

### Step 4: Calculate Total Cost of Purchase
Now, we can calculate the total cost of the purchase:
\[ \text{Total Cost} = \text{Total Cost of Laptops} + \text{Total Cost of Printers} = 75P + 15P = 90P \]

### Step 5: Calculate Percentage of Total Cost that is Laptops
To find the percentage of the total cost that is attributed to the laptops, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Total Cost of Laptops}}{\text{Total Cost}} \right) \times 100 \]
Substituting the values we calculated:
\[ \text{Percentage} = \left( \frac{75P}{90P} \right) \times 100 \]
The \( P \) cancels out:
\[ \text{Percentage} = \left( \frac{75}{90} \right) \times 100 = \frac{75 \times 100}{90} = \frac{7500}{90} = 83.33\% \]

### Final Answer
Thus, the percentage of the total cost of the purchase that was the total cost of laptops is approximately:
\[ \boxed{83.33\%} \]