Final answer:
The cost of a pen is $0.50.
Step-by-step explanation:
To find the cost of a pen, we can set up a system of equations based on the given information. Let's assume the cost of a pen is 'x' dollars. According to the problem, buying 5 pens and 6 pencils costs the same as buying 3 pens and 10 pencils. So we have the equation: 5x + 6(0.25) = 3x + 10(0.25). Simplifying this equation gives us: 5x + 1.5 = 3x + 2.5.
Next, we can subtract 3x from both sides of the equation to get: 2x + 1.5 = 2.5. Then, subtract 1.5 from both sides of the equation to get: 2x = 1. Finally, divide both sides of the equation by 2 to isolate x and solve for the cost of a pen: x = 1/2 = 0.5.
Therefore, the cost of a pen is $0.50.