Question

Claire and Richard are both artists. Claire uses the polynomial 50x^2+250 to decide how much to charge.Richard uses the polynomial 49x^2+350 to charge how much to charge for his painting.In each polynomial x is the height of the paintings feet. To the nearest tenth what height will both Claire and Richard charge for the same amount for a painting?

Answer 1

The height of the painting has to be 10 feet for both Claire and Richard to charge the same amount.

Explanation:

The polynomial expression representing the charge for Claire's paintings is:

C = 50x² + 250

The polynomial expression representing the charge for Richard's paintings is:

R = 49x² + 350

Here x represents the height of the paintings feet.

Now compute the value of x such that both Claire and Richard charge the same amount as follows:

C = R

50x² + 250 = 49x² + 350

50x² - 49x² = 350 - 250

x² = 100

x = 100

Thus, the height of the painting has to be 10 feet for both Claire and Richard to charge the same amount.