All tubes of watercolor paint at an art supply store have the the same price. An artist has a coupon for $0.50 off each tube of paint she buys. She buys 6 tubes of paint and pays a total of $84.30 after the coupon is applied. Write and solve an equation to find r, the regular price of each tube of paint. Expalin each step of your solution.

Let us assume the regular price of each tube of paint = r.

0.50 off each tube.

New price of each tube = r - 0.50.

She buy 6 tubes.

Total price of 6 tubes = 6 * (r-0.50).

We are given total price = $84.30.

Therefore, we can setup an equation

6 * (r-0.50) = 84.30.

Distributing 6 over (r-0.50), we get

6r - 3.0 = 84.30

Adding 3.0 on both sides, we get

6r - 3.0+3.0 = 84.30+3.0

6r = 87.30

Dividing both sides by 6, we get

6r/6 = 87.30/6

r = 14.55

Therefore, required equation is 6 (r-0.50) = 84.30 and the regular price of each tube of paint is $14.55.