Cost of Pens and Pencils Word Problem Solution

This problem requires us to find the combined cost of a specific number of pens and pencils, given their price relationship and a total purchase amount. We need to calculate the cost of 5 pens and 5 pencils.

Define Cost Variables

Let's represent the unknown costs using variables:

• Let the cost of one pencil be '$x$' rupees.
• The problem states that the cost of one pen is five times the cost of a pencil.
• Therefore, the cost of one pen is '$5x$' rupees.

Formulate Cost Equation

We are given that the purchase of 8 pens and 4 pencils cost Rs. 132.

• The total cost for 8 pens is $8 \times (\text{cost of one pen}) = 8 \times 5x = 40x$ rupees.
• The total cost for 4 pencils is $4 \times (\text{cost of one pencil}) = 4 \times x = 4x$ rupees.
• The sum of these costs equals the total amount spent:

$$40x + 4x = 132$$

Combining like terms:

$$44x = 132$$

Calculate Pencil Cost

To find the cost of a single pencil ('$x$'), we solve the equation:

Performing the division:

So, the cost of one pencil is Rs. 3.

Calculate Pen Cost

Now we find the cost of one pen using the relationship '$5x$':

Cost of one pen = $5 \times 3 = 15$ rupees.

Calculate Final Cost

The question asks for the cost of 5 pens and 5 pencils.

• Cost of 5 pens = $5 \times (\text{cost of one pen}) = 5 \times 15 = 75$ rupees.
• Cost of 5 pencils = $5 \times (\text{cost of one pencil}) = 5 \times 3 = 15$ rupees.
• The total cost for 5 pens and 5 pencils is the sum of their individual costs:

Total cost = $75 + 15 = 90$ rupees.

Thus, the cost of 5 pens and 5 pencils is Rs. 90.