SOLUTION: MR. Ramirez sells blue grass seed for $3.50 per pound and a fescue seed for $1.70 per pound. He wishes to make a 50 - pound mixture to sell for $2.96 per pound. Find how much of ea

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: MR. Ramirez sells blue grass seed for $3.50 per pound and a fescue seed for $1.70 per pound. He wishes to make a 50 - pound mixture to sell for $2.96 per pound. Find how much of ea      Log On


   

Question 188107: MR. Ramirez sells blue grass seed for $3.50 per pound and a fescue seed for $1.70 per pound. He wishes to make a 50 - pound mixture to sell for $2.96 per pound. Find how much of each kind of seed he nust use in the mixture

Let x = the number of pounds of bluegrass seed
let y=the number of fescue seed

x + y= 50
3.50 x + 1.70y= 2.96(50)

x +y =50
-3.50 -3.50y = -175
3.50 + 1.70y= 148
------------------------
-1.80y= -27 y=?

x+ ? =50
x=35 need a full break down of how my book got 35 i fell short from doing the problem

Found 2 solutions by Earlsdon, Mathtut:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Well, you got off to a good start with:
1) x+y = 50
2) 3.50x+1.70y = 2.96(50)
Now rewrite equation 1) as: x = 50-y and substitute this for x in equation 2).
2a) 3.50(50-y)+1.70y = 2.96(50) Simplfy this.
2b) 175-3.50y+1.70y = 148
2c) 175-1.8y = 148 Subtract 175 from both sides.
-1.8y = -27 Divide both sides by -1.8
y = 15 and...
x = 50-y
x = 50-15
x = 35
So, Mr. Ramirez needs to mix 35 lbs of Bluegrass seed @ $3.50 per lb. with 15 lbs of Fescue seed @ $1.70 per lb. to obtain 50 lbs of the mixture @ $2.96 per lb.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
let x and y be the number of pounds of blue grass and fescue respectively
:
x+y=50......eq 1
3.50x+1.7y=2.96(50)...eq 2
:
rewrite eq 1 to x=50-y and x's value of 50-y into eq 2 for all occurrences of x
:
3.5(50-y)+1.7y=148
:
175-3.5y+1.7y=148
:
-1.8y=-27
:
y=15 pounds
:
x=50-y=50-15=35 pounds