Fifty-three percent of a number is 358 less than the square of 26. What is the value of three-fourth of 32 percent of that number?

Let's break this down:

1. First, let's denote the unknown number as x. According to the problem, 53% of this number is 358 less than the square of 26. We can write this as an equation: 0.53x = 26^2 - 358.

2. Solve the equation for x. First, calculate the square of 26, which is 676. Then subtract 358 from 676, which gives 318. So, 0.53x = 318. To solve for x, divide both sides of the equation by 0.53. This gives x = 318 / 0.53 = 600.

3. Now that we know x = 600, we can find the value of three-fourth of 32 percent of that number. First, find 32% of 600, which is 0.32 * 600 = 192.

4. Finally, find three-fourth of 192, which is 0.75 * 192 = 144.

So, the value of three-fourth of 32 percent of the number is 144.