Solving the Math Problem: Cube Root and Percentage Equation

This problem requires us to find the value of the unknown variable, represented by a question mark ('?'), in the given equation. The equation involves a cube root and a percentage calculation.

The equation is:

$ \sqrt[3]{3375} \times 75\% \text{ of } 400 = \frac{?}{2} $

We need to solve this step-by-step:

Step 1: Calculate the Cube Root of 3375

First, let's find the cube root of 3375, denoted as $ \sqrt[3]{3375} $. We are looking for a number that, when multiplied by itself three times, equals 3375.

We can test some numbers. We know that $ 10^3 = 1000 $ and $ 20^3 = 8000 $. Since 3375 ends in 5, the cube root likely ends in 5. Let's try 15:

$ 15 \times 15 \times 15 = 225 \times 15 = 3375 $

So, the cube root of 3375 is 15.

$ \sqrt[3]{3375} = 15 $

Step 2: Calculate 75% of 400

Next, we need to calculate 75% of 400. The term "percent" means "per hundred", so 75% can be written as $ \frac{75}{100} $ or simplified to $ \frac{3}{4} $. Alternatively, we can use the decimal form, 0.75.

Using the fraction form:

$ 75\% \text{ of } 400 = \frac{75}{100} \times 400 $

$ = \frac{3}{4} \times 400 $

$ = 3 \times \frac{400}{4} $

$ = 3 \times 100 $

$ = 300 $

So, 75% of 400 is 300.

Step 3: Substitute and Solve for the Unknown

Now, we substitute the results from Step 1 and Step 2 back into the original equation:

$ 15 \times 300 = \frac{?}{2} $

First, calculate the product on the left side:

$ 15 \times 300 = 4500 $

The equation now becomes:

$ 4500 = \frac{?}{2} $

To find the value of '?', we need to isolate it. We can do this by multiplying both sides of the equation by 2:

$ 4500 \times 2 = \frac{?} {2} \times 2 $

$ 9000 = ? $

Conclusion

Therefore, the value that comes in place of the question mark is 9000.