an artist is going to an art fair. the artist will charge $20 for small prints $45 for large prints. the artist would like to sell twice as many small prints as large prints. the booth the artist is renting costs $510. how many of each size print must the artist sell in order to break even at the fair?

For each large print, he sells small prints. For the three prints, he makes 45+2*20=85$.

Rent = 510
He must sell 510/85=6 sets of three prints, or 6 large and 12 small prints to break even.

To determine how many of each size print the artist must sell to break even, let's set up an equation:

Let's denote the number of small prints as "x" and the number of large prints as "y".

Given the information:
- The artist charges $20 for small prints and $45 for large prints.
- The artist wants to sell twice as many small prints as large prints.

We know that the total cost (or expenses) for the artist is $510, which includes the booth rental.

To break even, the total revenue from selling prints should cover the booth cost.

The revenue from selling small prints (x) is: $20 * x.
The revenue from selling large prints (y) is: $45 * y.

We need to find the values of x and y that satisfy the equation:

$20 * x + $45 * y = $510

Additionally, we know that the artist wants to sell twice as many small prints as large prints:

x = 2y

Now we can solve the system of equations:

Substitute x in terms of y:
$20 * (2y) + $45 * y = $510

Simplify the equation:
$40y + $45y = $510
$85y = $510

Now solve for y:
y = $510 ÷ $85
y = 6

So, the artist needs to sell 6 large prints.

Now substitute the value of y back into the equation for x:
x = 2y
x = 2 * 6
x = 12

Therefore, the artist needs to sell 12 small prints.

To summarize, the artist must sell 12 small prints and 6 large prints in order to break even at the art fair.