Track / Stage 3 / 6 of 260 #6 of 1964

Problem 6

AMC 10/12, early questions

Algebra Difficulty 3.0 Find the answer

A certain medicine underwent two price reductions, with the retail price per bottle decreasing from $58 to$ 43. Given that the percentage reduction for both price reductions is $x$ , the equation to be written is ______. (Write down the equation only, do not solve it)

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Given the initial price of the medicine is 58 and it undergoes two successive price reductions by the same percentage x, the price after the first reduction is 58(1-x). Since there is a second reduction by the same percentage, we apply the reduction again to the new price, resulting in 58(1-x)(1-x) $or$ 58(1-x)^2 as the final price. This final price is given as 43.

Therefore, the equation representing this situation is:

$58(1-x)^2 = 43$

So, the equation to be written is $\boxed{58(1-x)^2 = 43}$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.