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Ivan spends $117.30 on painting supplies plus $9.50 for each canvas he paints. He sells his paintings for $18 each. Let m be the amount of money in dollars and p be the number of paintings produced. The system of equations that models the scenario is: m = 9.5p + 117.3 m = 18p How many paintings does Ivan need to sell in order to start making a profit?

Respuesta :

ivan needs to sell 14 paintings.

Answer:

He need to sell 14 paintings.

Step-by-step explanation:

Here, p represents the number of produced paintings,

Total amount spent on painting supplies = $ 117.30,

Also, the cost of each canvas he paints = $ 9.50,

Thus, the total cost of the p paintings = ( 117.30 + 9.50x ) dollars,

Now, selling price of one painting = $ 18,

So, the selling price of x paintings = 18x dollars,

Since, he will earn profit,

If, Selling price of the paintings - Cost price of the painting > 0

⇒ 18x - (117.30 + 9.50x) > 0

⇒ 8.50x - 117.30 > 0

⇒ 8.50x > 117.30

⇒ x > 13.8

Hence, he need to sell 14 paintings for making the profit. ( number of painting must be an integer )