Math
posted by Jamese on .
A coffee dealer mixed 12 pounds of one grade coffee with 10 pounds of another grade of coffee to obtain a blend worth $54. He then made a second blend worth $61 by mixing 8 pounds of the first grade with 15 pounds of the second grade. Find the price per pound of each grade.

first grade  x lbs
2nd grade  y lbs
12x + 10y = 54 > 6x+5y = 27
8x + 15y = 61
1st equation times 3
18x + 15y = 81
8x + 15y = 61
subtract them
10x = 20
x = 2
sub back into 6x+5y=27
12+5y=27
y = 3
1st grade is $2 per pound, 2nd grade is $3 per pound
(coffee at $2 a pound!!! WOW, time to update that texbook) 
define Variables,
Grade#1=x
Grade#2=y
total cost=z
a=pounds of Grad#1
b=pounds of Grade#2
write equation,
z=ax+by
Define values
12 pounds Grade1 and 10 pounds of Grade2 worth $54; 8 pounds Grade1 and 15 pounds Grade2 worth $61
Plug in values, isolate one variable,
54= 12x+10y , 61= 8x+15y
12x=12x , 8x=8x
5412x=10y , 618x=15y
(5412x)/10=(10y)/10 , (618x)/15=
(5412x)/10x=y , (15y)/15
(276X)/5=y , (618x)/15=y
set equations equal to each other, solve for remaining variable,
(276x)/5=(618x)/15
*15=*15
3(276x)=618x
8118x=618x
+18x= +18x
81=61+10x
61=61
20=10x
(20)/10=(10x)/10
2=y
Pick one equation, Plug in new value, solve for last variable,
54=12x+10y
54=12x+10*(2)
54=12x+20
20= 20
34=12x
(34)/12=(12x)/12
(17/6)=x
2.83=x
Grade one is $2/lb
Grade two is $2.83/lb