From the two purchases, you should get two equations involving the same two variables. Write both equations clearly and check that the coefficients (the numbers in front of the variables) match the description of each purchase.

Think about how to remove one variable. Can you multiply one or both equations so that the coefficients of either the corn or the fertilizer match, allowing you to subtract the equations?

After you eliminate one variable, you will get a single equation with only the fertilizer variable. Solve this equation carefully, then match your result to the closest answer choice.

In Desmos, type the two equations as:

• 3x + 2y = 128
• 5x + 6y = 268 Here, let $x$ represent the cost of one bag of corn seed and $y$ represent the cost of one bag of fertilizer.

Look at the graph and find the point where the two lines intersect. Click on that intersection; Desmos will display its coordinates $(x, y)$.

The $y$-coordinate of the intersection gives the value of $y$, which is the cost of one bag of fertilizer in dollars. Match that value to the correct answer choice.

Let:

• $c$ = cost (in dollars) of one bag of corn seed
• $f$ = cost (in dollars) of one bag of fertilizer

Translate each purchase into an equation:

• First purchase (3 corn, 2 fertilizer, total $128): $3c + 2f = 128$
• Second purchase (5 corn, 6 fertilizer, total $268): $5c + 6f = 268$

We want to eliminate one variable to solve the system quickly. Eliminate $c$ by making the coefficients of $c$ in both equations match.

Multiply the first equation by $5$ and the second equation by $3$ so both will have $15c$:

• First equation

• Second equation

Now subtract the first new equation from the second new equation to eliminate $c$:

Now solve the equation $8f = 164$ for $f$:

So one bag of fertilizer costs $20.50.

The correct answer choice is C) 20.50.