what is the length of the pasture?

Question

the width of a pasture is 40 yards more than twice its length. if the area is 2250 square yards what is the length of the pasture?

Answer 1

To solve this problem you need to write equations and then solve the 'system' of equations.
If you look at the problem you will see there are at least 2 unknown things
(the Length and Width) so we will need two equations.
If more unknown things come up when we are working on the problem we will need more equations.

Lets call the length 'L' and the width 'W'
- you can pick anything for the symbols but those are easy to remember.

Now lets look at the English sentences and see if we can translate those into our Maths language.

The width is 40 yards more than twice its length.
W = 40 yards more than (2 x L)

    = 40 yds + 2L

The area is 2250 Square yards.
Do you know the way to calculate the area? Multiply length times width.
A = 2250 Sq Yds = L x W

There are different ways to solve systems of equations.
One way is to solve 1 equation to have 1 variable on one side = an expression of the other variable.
But one of our equations is already that way: W = 40 yds + 2L

Now substitute that into the other equation and solve it.
W = 2L + 40 yds
A = 2250 Sq Yds = L x W = L x (2L + 40 yds)
I hope you see where this is going.
2250 Sq Yds = L x (2L + 40 yds) = 2L^2 + (L x 40 yds)

Find L. Then use that to find W.

Comment to let us know how it goes, if you get stuck,
or if you want someone to check your answer.

Answer 2

W = 2L + 40

 

A = 2250 = WL = L(2L + 40)

 

2L^2 + 40L - 2250 = 0

 

L^2 + 20L - 1125 = 0

 

-25(45) , -25+45=20

 

(L^2 – 25L) + (45L - 1125) = 0

 

L(L – 25) + 45(L – 25) = 0

 

(L – 25)(L + 45) = 0

 

L = 25 or L = -45; but L > 0, so

 

L = 25.