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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineKurt, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for $18\$18, and paint and canvas for each painting costs $79\$79; he will sell each painting for $85\$85. Once Kurt sells a certain number of his paintings, he will be breaking even. How many paintings will that be? How much will Kurt have earned?\newlineOnce Kurt has sold _____ paintings, his expenses and receipts will both equal $\$_____.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineKurt, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for $18\$18, and paint and canvas for each painting costs $79\$79; he will sell each painting for $85\$85. Once Kurt sells a certain number of his paintings, he will be breaking even. How many paintings will that be? How much will Kurt have earned?\newlineOnce Kurt has sold _____ paintings, his expenses and receipts will both equal $\$_____.
  1. Define Variables: Define the variables and write the equations.\newlineLet xx be the number of paintings Kurt sells.\newlineKurt's expenses for xx paintings include the initial cost of brushes and the cost of paint and canvas for each painting.\newlineTotal expenses == Cost of brushes ++ (Cost of paint and canvas per painting ×\times Number of paintings)\newlineTotal expenses =18+79x= 18 + 79x
  2. Calculate Expenses: Kurt's earnings from selling xx paintings will be the selling price per painting times the number of paintings sold.\newlineTotal earnings = Selling price per painting ×\times Number of paintings\newlineTotal earnings = 85x85x
  3. Calculate Earnings: To break even, Kurt's total expenses must equal his total earnings.\newlineSet the total expenses equal to the total earnings and solve for xx.\newline18+79x=85x18 + 79x = 85x
  4. Set Equation: Subtract 79x79x from both sides of the equation to isolate the variable on one side.\newline18+79x−79x=85x−79x18 + 79x - 79x = 85x - 79x\newline18=6x18 = 6x
  5. Isolate Variable: Divide both sides of the equation by 66 to solve for xx. \newline186=6x6\frac{18}{6} = \frac{6x}{6}\newline3=x3 = x
  6. Solve for x: Calculate the total earnings when Kurt has sold 33 paintings.\newlineTotal earnings = 85x85x\newlineTotal earnings = 85×385 \times 3\newlineTotal earnings = $255\$255

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