Translate the sentence "the number of large prints sold was 9 more than the number of small prints sold" into an equation involving $x$ and $y$. Which variable should be on each side?

Once you have equations for the total money and for the relationship between $x$ and $y$, use substitution: replace $y$ in the money equation with an expression in terms of $x$, then solve for $x$.

After you find $x$, use the relationship between $x$ and $y$ to find $y$. Make sure your final answer matches the quantity the question asks for: the number of large prints.

In Desmos, type the two equations from the problem:

1. 4x + 7y = 250
2. y = x + 9 Desmos will graph both lines on the coordinate plane.

Look for the point where the two lines intersect. Click on the intersection point; Desmos will display its coordinates $(x, y)$.

The $x$-coordinate of the intersection represents the number of small prints, and the $y$-coordinate represents the number of large prints. Use the $y$-value shown at that intersection as your final answer.

Small prints cost $4 each and large prints cost $7 each. If $x$ is the number of small prints and $y$ is the number of large prints, then the total money earned is

because $4x$ is the money from small prints and $7y$ is the money from large prints.

The problem says "the number of large prints sold was 9 more than the number of small prints sold."

That means the number of large prints $y$ is 9 more than the number of small prints $x$, so we write:

Now we have a system of two equations with two variables.

Since $y = x + 9$, substitute $x + 9$ in place of $y$ in the money equation.

Start with

Substitute $y = x + 9$:

Now simplify the left side:

Solve the equation from the previous step:

This means 17 small prints were sold. The number of large prints is

So, the studio sold 26 large prints.