Answer: 9m^3 of soil with 50% clay and 2m^3 of soil with 28% clay is required
Explanation:
Let x represent the quantity of the soil containing 50% clay that you would use.
Let y represent the quantity of the soil containing 28% clay that you would use.
To build the garden of your dreams you need 11 m^3 of soil.
x + y = 11 - - - - - - - - -1
Since the soil must contain 46% clay, the total amount of clay required is 46/100 × 11 = 5.06 m^3.
you have two types of soil you can combine to achieve this: soil with 50% clay and soil with 28% clay. This means that the quantity of both soils required to achieve 5.06 m^3 will be
0.5x + 0.28y = 5.06 - - - - - - - -2
Substituting x = 11 - y into equation 1, it becomes
0.5(11 - y) + 0.28y = 5.06
5.5 - 0.5y + 0.28y = 5.06
- 0.5y + 0.28y = 5.06 - 5.5
- 0.22y = - 0.44
y = - 0.44/ -0.22 = 2
Substituting y = 2 into x = 11 - y, it becomes
x = 11 - 2 = 9