If a 10-kilogram soil mixture contains 30% sand, how many kilograms of the mixture should be removed to achieve 50% sand?

To determine how many kilograms of the soil mixture should be removed to achieve a 50% sand concentration, we first need to analyze the current composition of the mixture.

Initially, the 10-kilogram mixture contains 30% sand. We can calculate the weight of the sand in the mixture by using the formula:

Weight of sand = Total weight of mixture × Percentage of sand = 10 kg × 0.30 = 3 kg.

This means that the mixture has 3 kilograms of sand and, consequently, 10 kg - 3 kg = 7 kg of other materials (such as soil or clay).

Let’s denote the amount of mixture to be removed as x kilograms. After removing x kilograms, the new total weight of the mixture will be (10 - x) kilograms. The weight of sand remains unchanged at 3 kilograms because the sand is only removed along with the other material when the mixture is taken out.

To achieve a situation where 50% of the remaining mixture is sand, we set up the equation:

(Weight of sand) / (New total weight) = 50%.

Substituting the known values, we have:

3 kg / (10 - x) kg = 0.50