Claire and Richard are both artists who use square canvases. Claire uses the polynomial 50%? + 250 to decide how much to charge for her paintings

and Richard uses the polynomial 40x² + 350 to decide how much to charge for

his paintings. In each polynomial, x is the height of the painting in feet.

a. How much does Claire charge for a 20-foot-tall painting?

b. How much does Richard charge for a 15-foot-tall painting?

c. To the nearest tenth, for what height will both Claire and Richard charge

the same amount for a painting? Explain how to find the answer.

d. When both Claire and Richard charge the same amount for a painting,

how much does each charge?

A.  

B.  

C.    Height = 3.2 feet

D. Charges = $760

Step-by-step explanation:

Given

Solving (a): Claire's 20ft charges

In this case, x = 20

Substitute 20 for x in

Solving (b): Richard's 15ft charges

In this case, x = 15

Substitute 20 for x in

Solving (c): Height which they both charge the same;

This implies that

Solving for x [Collect Like Terms\

Divide both sides by 10

Take square roots of both sides

 (Approximated)

Hence; Height = 3.2 feet

Solving (d): How much they charge when the charge the same amount.

Substitute 3.2 for x in any of the given equation

The reason for the difference is due to approximation

Hence, they both charge approximately 760

b.an increase in a causes b to decrease