compost costs $10 per cubic yard and topsoil costs $2 per cubic yard. maria needs more than 10 cubic yards…

Explanation:

Step1: Define cost - function

Let $x$ be the number of cubic yards of compost and $y$ be the number of cubic yards of top - soil. The cost function is $C = 10x+2y$, and the constraints are $y>10$ and $C\leq50$, i.e., $10x + 2y\leq50$ or $5x + y\leq25$.

Step2: Check option 1

For $x = 2$ and $y = 8$, since $y=8<10$, it does not satisfy $y > 10$, so this option is incorrect.

Step3: Check option 2

For $x = 4$ and $y = 5$, since $y = 5<10$, it does not satisfy $y>10$, so this option is incorrect.

Step4: Check option 3

For $x = 1$ and $y = 12$: First, $y = 12>10$. Second, calculate the cost $C=10\times1 + 2\times12=10 + 24=34$. And $34\leq50$. So this option satisfies the constraints.

Step5: Check option 4

For $x = 3$ and $y = 12$, calculate the cost $C=10\times3+2\times12=30 + 24 = 54$. Since $54>50$, it does not satisfy $10x + 2y\leq50$, so this option is incorrect.

Answer:

1 cubic yard of compost, 12 cubic yards of topsoil