Question

I can only use 1 variable to write and solve an equation for the following question: "The length of a rectangular field is 10 meters less than 4 times its width. It costs $1584 to put a fence around the field. If the fencing costs $4.80 per meter, what is the area of the field?" What is my equation? (only 1 variable!)

Answer 1

Assume w to be the width (the one variable we will use is w).
What is the length?

Answer 2

The length is not given. I have to find the length and the width based on the price of each meter for fencing and the total price.

Answer 3

No. From the problem description you can first derive the length in terms of the variable w.
If width = w
length = 4w - 10 ("The length of a rectangular field is 10 meters less than 4 times its width.")
Now Perimeter = ? (use the width and length in the previous two lines)
Perimeter =

Answer 4

Would my equation (in simplest form) be 5w - 10?

Answer 5

There are two length and two widths to a rectangle. So the perimeter will be the sum of all four sides.

Answer 6

So it would be 10w -20? And also, I need to know what it would equal. (Ex. 10w-20=?)

Answer 7

Yes we will get to that. I am just doing a step-by=step walk through.
So the perimeter = 10w - 20. Keep this aside for the time being.

Reading the problem further we can find the numerical value of the perimeter.

It costs $4.80 per meter and the total cost to put the fence around the perimeter is $1584. So how many meters is the perimeter based on these two numbers?

Answer 8

The perimeter is 330 meters.

Answer 9

Yes. Now we calculated the perimeter earlier at 10w - 20 = 330.
Solve for w.

Answer 10

w = 35

Answer 11

And length = ?

Answer 12

The length is 130 meters

Answer 13

Area = ?

Answer 14

The area is 4550 meters

Answer 15

Yep!

Answer 16

Thank you so much for all of your help!

Answer 17

no problem.