Let C denote the quantity of compost
T represent the quantity of topsoil
Each cubic yard of compost is priced at $25
Thus, the cost of C cubic yards of compost is 25C
Each cubic yard of topsoil costs $15
Therefore, the cost for T cubic yards of topsoil is 15T
Together, the amount of compost plus topsoil equals 10
C + T = 10 -------> Equation 1
The total cost for compost and topsoil is $180
25C + 15T = 180 --------> Equation 2
Rearranging the first equation to find C
C + T = 10
results in
C = 10 - T
Now substitute into the second equation
25C + 15T = 180
25 ( 10 - T) +15T = 180
Using like terms: 250 - 25T + 15T = 180
From which we can simplify to 250 - 10T = 180 by removing 250 from both sides
-10T = 180 - 250
yielding -10T = -70 (dividing both sides by -10)
results in T = 7