Ellie would like to build the garden of her dreams. she needs 27 cubic feet of soil containing 12% clay. she has 2 types of souls that she can combine to achieve this: soil with 27% clay and soil with 15% clay. how much of each should she use?

To determine how much she should use for every type of soil, we need to set up equations. We do as follows:

Let x = amount of the soil with 27% clay
      y = amount of the soil with 15% clay

We have two unknowns so we need two equations. 

First equation,

x + y = 27

Second equation,

.27x + .15y = (27)(.12)
.27 + .15y = 3.24

Solving x and y,
x = -6.75
y =33.75

Since we have a value that is negative, it would be impossible to make a 12% clay soil with the given soils.