Question 5

The price of each shirt is 75 - n/2 dollars.

To find the price of each shirt in terms of n, we start by setting up the equation based on John's purchases. He bought 2 shirts and 1 pair of pants for a total of 75 dollars, where the pants cost n dollars. This leads us to the equation 2s + n = 75, allowing us to solve for the price of each shirt (s) as 75 - n/2.

A) 75/2

This option suggests that each shirt costs 75/2 dollars, which would imply that the total for two shirts is 75 dollars. However, this does not account for the cost of the pants, leading to an incorrect total that does not match the given information.

B) 75 + n/2

This option indicates that each shirt costs 75 + n/2 dollars. If this were the case, the total cost for two shirts would exceed the total of 75 dollars when the cost of the pants is included, making this option impossible within the constraints of the problem.

C) 75 - n/3

This choice suggests that each shirt is priced at 75 - n/3 dollars. However, substituting this into the equation for total cost would not yield a valid solution, as it would lead to a total that does not satisfy the original equation of 2s + n = 75.

D) 75 - n/2

This option accurately represents the relationship established by the equation derived from John's purchases. By substituting the expression for s back into the equation, we confirm that the total cost of the two shirts and the pants indeed totals 75 dollars, validating this choice as correct.

Conclusion

The correct answer, 75 - n/2, provides a clear and precise calculation of the price of each shirt based on the total expenditure of 75 dollars and the cost of the pants. All other options misinterpret the relationship between the cost of the shirts and pants, leading to incorrect totals that do not align with the scenario presented.