Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Omar, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for $5, and paint and canvas for each painting costs $67; he will sell each painting for $68. Once Omar sells a certain number of his paintings, he will be breaking even. How much will Omar have earned? How many paintings will that be? Omar's expenses and receipts will both total $_____ when he has sold _____ of his paintings.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Omar, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for $5, and paint and canvas for each painting costs $67; he will sell each painting for $68. Once Omar sells a certain number of his paintings, he will be breaking even. How much will Omar have earned? How many paintings will that be?   Omar's expenses and receipts will both total $_____ when he has sold _____ of his paintings.

Bytelearn · Accepted Answer

Define Expenses Equation: Let x represent the number of paintings Omar sells. His expenses include the initial cost of brushes and the cost of paint and canvas for each painting. His income comes from selling each painting. We need to find the point where his expenses equal his income, which is the break-even point.Calculate Income: The cost of brushes is a one-time expense of $5. The cost of paint and canvas for each painting is $67, so the total cost for x paintings is $67x. Therefore, the equation for Omar's expenses (E) is: E = 67x + 5Set Break-Even Point: Omar sells each painting for $68, so his income (I) from selling x paintings is: I = 68xSolve for x: To find the break-even point, we set the expenses equal to the income: 67x + 5 = 68xSubstitute x into Income: Now we solve for x by subtracting 67x from both sides of the equation: 67x + 5 - 67x = 68x - 67x 5 = xFinal Answer: We found that x = 5, which means Omar needs to sell 5 paintings to break even. To find out how much Omar will have earned at this point, we substitute x into the income equation: I = 68x I = 68(5) I = $340Omar's expenses and receipts will both total $340 when he has sold 5 of his paintings. This answers the question prompt.

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