Jasmin paints a border around the wall in her room. The border will be 60 feet long. She has enough paint to cover 15 square feet.

a. If the border is 1/3 foot wide, how much of the border can she cover with paint?

(1/3) L = 15

so
L = 45 feet long border but we need 60 not 45
so we can only paint 45/60 = 3/4 = 75% of the border

To find out how much of the border Jasmin can cover with paint, we first need to calculate the area of the border. The border is a strip that goes around the entire room, and its width is 1/3 foot.

The length of the border is given as 60 feet. Since the border goes all the way around the room, the width is the same as the height of the room. Let's call the height of the room h.

The formula for the perimeter of a rectangle is P = 2h + 2w, where P is the perimeter, h is the height, and w is the width. In this case, we want to find the width, so we can rearrange the formula to solve for w:

w = (P - 2h) / 2

Substituting the given values:

w = (60 - 2h) / 2

Since the width is 1/3 foot, we can set up the equation:

1/3 = (60 - 2h) / 2

Next, we can solve for h:

Multiply both sides of the equation by 2 to get rid of the fraction:

2/3 = 60 - 2h

Subtract 60 from both sides:

-58/3 = -2h

Divide by -2:

58/6 = h

Simplify the fraction:

29/3 = h

So the height of the room is 29/3 feet.

Now we can calculate the area of the border. The area of a rectangle is given by the formula A = w * h. In this case, the width is 1/3 foot and the height is 29/3 feet:

A = (1/3) * (29/3)

Multiply the fractions:

A = 29/9

Therefore, the area of the border is 29/9 square feet.

Lastly, we can determine how much of the border Jasmin can cover with paint. She has enough paint to cover 15 square feet, and the area of the border is 29/9 square feet. To find the fraction of the border she can cover, we divide the area she can cover by the total area:

Fraction covered = (15)/(29/9)

To divide by a fraction, we multiply by its reciprocal:

Fraction covered = (15) * (9/29)

Multiply the numbers:

Fraction covered = 135/29

Therefore, Jasmin can cover approximately 135/29 of the border with paint.