Question

Q decreased by P% equals t. What is t in P and Q and what terms is Q in the terms P and t?

a) t = (P/100) * Q, Q in P and t
b) t = (100/P) * Q, Q in t and P
c) t = (Q/P) * 100, Q in P and t
d) t = (Q/100) * P, P in Q and t

Answer 1

The correct expression for t when Q decreases by P% is t = Q(1 - P/100), and for Q in terms of P and t is Q = t / (1 - P/100). The given answer choices do not include this correct formula. This is a high school level mathematics problem involving percentages.

Step-by-step explanation:

The question presents a scenario where Q decreased by P% results in t. To find t, you would take Q and diminish it by P%. This means you subtract the P% of Q from Q itself, which algebraically is expressed as t = Q - (P/100) × Q. Simplifying this, you end up with t = Q(1 - P/100), which is not explicitly stated in the given options.

Conversely, if you have t and need to express Q in terms of P and t, you'd solve the previous equation for Q, resulting in Q = t / (1 - P/100). None of the options provided (a through d) correctly represents these relationships. Therefore, the correct calculation is not listed among the options.

It is also important to understand that if a % change in Price is exactly offset by a corresponding % change in Quantity, the total revenue (Price × Quantity) remains unchanged. However, this fact is not directly needed to solve for t in this specific problem.