Problem 5

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 $\boxed{58(1-x)^2 = 43}$.