SOLUTION: Write a system of equations for the following: A rectangle is 3times longer than it's width. The permiter is 44 cm. A farmer grows only pumpkins & corn on a 420 acre farm. He

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Write a system of equations for the following: A rectangle is 3times longer than it's width. The permiter is 44 cm. A farmer grows only pumpkins & corn on a 420 acre farm. He      Log On


   

Question 252149: Write a system of equations for the following:
A rectangle is 3times longer than it's width. The permiter is 44 cm.
A farmer grows only pumpkins & corn on a 420 acre farm. He wants to plant 250 more acres of corn than of umpkins. How many acres of each crop does he need to plant.
I figured the answers but do not know how to write a system of equations for them
Answer by blwinbbbles(106) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, the easiest way to do this is to write down what you have:

(1)
L = length W=width
if a rectangle is 3 times longer than wide you know:
L = 3W
and if the perimeter of a rectangle is all the sides added up you can say.
L+L+W+W=perimeter or 2L + 2W = perimeter.
so your two equation for the first system are:
L = 3W
2L + 2W = 44 use substitution
2(3W) + 2W = 44
6W + 2W = 44
8W = 44
w = 5.5cm so sub back into orginal equation L=3W
L= 3(5.5) = 16.5 cm

(2)
p=pumpkin c=corn
we know that together he wants 420 acres of both so:
p+c=420
and he wants 250 more acres of corn than pumpkin so
p=c+250
So your two equations are:
p+c=420
c=250+p
Use substitution again
p + p + 250 = 420 Subtract 250 from both sides
2p = 170 divide both sides by 2
p=85acres
Sub back into orginal equation
c=250+85
c= 335acres
hope this helps