An artist wishes to frame a picture with 84 inches of framing material. How wide will the frame be if its width if 75% of its length?
W = .75L
84 = 2W + 2L = 2(.75L) + 2L = 3.5L
L = 24
.75L = 18 = W
To find the width of the frame, we first need to determine its length. Let's assume the length of the frame is represented by the variable "x".
According to the problem, the width of the frame is 75% of its length. This can be expressed as 0.75x.
We are also given that the total amount of framing material available is 84 inches. The framing material consists of the four sides of the frame, so the total length of the framing material is equal to the perimeter of the frame.
The formula for the perimeter of a rectangle is P = 2*(length + width). Considering that a frame is essentially a rectangle, we can calculate the perimeter of the frame:
84 = 2*(x + 0.75x)
Now, we can simplify and solve the equation for x:
84 = 2*(1.75x)
84 = 3.5x
Divide both sides of the equation by 3.5:
84/3.5 = x
24 = x
Therefore, the length of the frame is 24 inches.
To find the width of the frame, we can substitute the value for x into the equation for the width:
Width = 0.75x = 0.75*24 = 18
Thus, the width of the frame will be 18 inches.