Question

Aliyah and her brother mixed together two

types of soil to make 15 m³ of soil with a
32% clay content. They used 6 m³ of a
soil with 56% clay content and 9 m³ of
another type of soil. What was the clay
content of the second type of soil?

Answer 1

To find the clay content of the second type of soil, an equation is set up with the known volume and clay content from both types of soils. Solving the equation yields a clay content of 16% for the second type of soil.

Step-by-step explanation:

To solve the problem of determining the clay content of the second type of soil used by Aliyah and her brother, we need to set up an equation based on the total volume and percentage of clay in the soils mixed together. We know that 6 m³ of soil with a 56% clay content is mixed with 9 m³ of another type of soil to make 15 m³ of soil with a 32% clay content overall.

First, calculate the total amount of clay in the 6 m³ of the first type of soil:

• Amount of clay in first type of soil = 6 m³ * 56% = 3.36 m³ of clay

Let the clay content of the second type of soil be x. Then, the amount of clay in the second type of soil is:

• Amount of clay in second type of soil = 9 m³ * x

According to the problem, the total amount of clay in the 15 m³ of mixed soil is:

• Total clay content = 15 m³ * 32% = 4.8 m³ of clay

Now we can set up the equation to find x:

1. 3.36 m³ + (9 m³ * x) = 4.8 m³
2. 9 m³ * x = 4.8 m³ - 3.36 m³
3. 9 m³ * x = 1.44 m³

Divide both sides of the equation by 9 m³ to solve for x:

• x = 1.44 m³ / 9 m³
• x = 0.16 or 16%

Therefore, the clay content of the second type of soil is 16%.