Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store. If Jay bought 3 pens and 5 pencils, and Vijay bought 2 pens and 7 pencils, then which one of the following is correct?

Correct Answer: The price of a pen is two times the price of a pencil

Step-by-step Explanation:

Let us define variables for the cost of each item:

Let $x$ be the cost of one pen.

Let $y$ be the cost of one pencil.

1. Formulate expressions for total money spent:

Jay bought 3 pens and 5 pencils, so the total amount spent by Jay is:

$\text{Jay's total spend}=3x+5y$

Vijay bought 2 pens and 7 pencils, so the total amount spent by Vijay is:

$\text{Vijay's total spend}=2x+7y$

2. Set up the equation:

Since Jay and Vijay spent an equal amount of money, we can equate the two expressions:

$3x+5y=2x+7y$

3. Solve for $x$ in terms of $y$:

Subtract $2x$ from both sides of the equation:

$3x-2x+5y=7y$

$x+5y=7y$

Now, subtract $5y$ from both sides:

$x=7y-5y$

$x=2y$

Conclusion:

The price of one pen ($x$) is equal to two times the price of one pencil ($y$).