At a clothing store, John bought 2 equally priced shirts and 1 pair of pants. The price of the pants was n dollars, and the total price for the 3 items was 75 dollars. What was the price, in dollars, of each of the shirts in terms of n?

Rationale

Each shirt costs 75 - n/2 dollars.

To determine the price of each shirt in terms of n, we start with the total cost equation: 2s + n = 75, where s represents the price of one shirt. By isolating s, we can express it directly in terms of n.

A (75/2) YOUR ANSWER

This option suggests that each shirt costs 37.5 dollars, which does not consider the cost of the pants. If we set s = 75/2, then the total cost would be 2(75/2) + n = 75, leading to a total cost of 75 dollars without factoring in the price of the pants. Thus, this choice is incorrect.

B (75 + n/2) YOUR ANSWER

This choice implies that the price of each shirt exceeds the total combined price of all items. If s = 75 + n/2, then the total cost would be 2(75 + n/2) + n, which would exceed 75 dollars, as it incorrectly adds the cost of the pants to the already inflated shirt price. Therefore, this option is also incorrect.

C (75 - n/3) YOUR ANSWER

If each shirt costs 75 - n/3, the total cost becomes 2(75 - n/3) + n. Simplifying this results in 150 - 2n/3 + n = 150 + n/3, which cannot equal 75 for any positive n. This shows that the calculation does not satisfy the original total, making this option incorrect.

D (75 - n/2) CORRECT

This option correctly derives the cost of each shirt. Starting from the equation 2s + n = 75, we isolate s: 2s = 75 - n, leading to s = (75 - n)/2. This matches our derived expression, confirming that each shirt costs 75 - n/2 dollars.

Conclusion

In summary, the correct expression for the price of each shirt, given the conditions of the problem, is 75 - n/2 dollars. This formulation accurately reflects the total cost constraints while ensuring that the price of the shirts and pants aligns with the total expenditure of 75 dollars.

At a clothing store, John bought 2 equally priced shirts and 1 pair of pants. The price of the pants was n dollars, and the total price for the 3 items was 75 dollars. What was the price, in dollars, of each of the shirts in terms of n?

Each shirt costs 75 - n/2 dollars.

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