He spent $48 on art supplies. The canvas for each of his paintings is an additional $2. He plans to sell his paintings for $10. Find the number of paintings (p) he will need to sell to break even.
48 + 2p = 10p
48 = 8p
6 = p
To find the number of paintings he needs to sell to break even, we need to set up an equation.
Let's first calculate the cost of the art supplies for each painting. We know that the canvas for each painting costs an additional $2, and since he spent $48 on art supplies, we can subtract the cost of the canvas from the total amount to find the cost of other supplies.
The cost of other supplies = Total art supplies cost - Cost of canvas
The cost of other supplies = $48 - $2
The cost of other supplies = $46
Now, let's set up the equation to find the number of paintings needed to break even:
Total cost = Total art supplies cost + Total amount he plans to sell the paintings for
Since the total cost is the cost of other supplies plus the cost of the canvas for each painting (which is $2), we can write this equation as:
Total cost = $46 + $2p
(where p represents the number of paintings to break even)
The total amount he plans to sell the paintings for is $10 per painting, multiplied by the number of paintings (p):
Total amount he plans to sell the paintings for = $10p
To break even, the total cost must be equal to the total amount he plans to sell the paintings for:
$46 + $2p = $10p
Now, we can solve this equation to find the value of p, the number of paintings he needs to sell to break even.
$46 + $2p - $2p = $10p - $2p
$46 = $8p
To isolate p, divide both sides of the equation by $8:
$46/$8 = $8p/$8
5.75 = p
Therefore, he will need to sell approximately 5.75 paintings (which we can round up to 6) to break even.