Please help I've been stuck on this for hours 10. Write an inverse variation to model the situation and answer the question. Two rectangular fields have the same area. One measures 75 yd by 60 yd. If the other has a length of 72 yd, what is its width?.
A = Area
w = width
l = length
A = w ∙ l
Divide both sides by l
A / l = w
w = A / l
Find the value of A by substituting the given information:
w = 60 yd
l = 75 yd
A = w ∙ l = 60 ∙ 75
A = 4500 yd²
Substitute l = 72 yd to find the width of the second field:
w = A / l
w = 4500 / l = 4500 / 72 = 62.5 yd
Thank you so much!!
To solve this problem, we need to understand the concept of inverse variation. Inverse variation occurs when two variables have a constant product. In mathematical terms, if x and y are inversely proportional, then their product xy remains constant.
To model the situation in this problem, we can use the formula for the area of a rectangle: Area = Length * Width.
Let's express the inverse variation relationship between the length and width of the rectangles:
Length * Width = k
Here, k represents the constant of variation.
Now, we can set up an equation using the given information:
For the first rectangle: Length = 75 yd and Width = 60 yd, so we have 75 * 60 = k.
To find the constant of variation (k), we multiply the given length and width.
k = 75 * 60
k = 4500
Now, we can use the constant of variation (k) to find the width of the second rectangle, given that its length is 72 yards.
Let's represent the width of the second rectangle as x:
72 * x = k
72 * x = 4500
To find the value of x, we divide both sides of the equation by 72:
x = 4500 / 72
x = 62.5
Therefore, the width of the second rectangular field is 62.5 yards.