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
10x = 20
x = 2
sub back into 6x+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)
a=pounds of Grad#1
b=pounds of Grade#2
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
54-12x=10y , 61-8x=15y
(54-12x)/10=(10y)/10 , (61-8x)/15=
(54-12x)/10x=y , (15y)/15
(27-6X)/5=y , (61-8x)/15=y
set equations equal to each other, solve for remaining variable,
Pick one equation, Plug in new value, solve for last variable,
Grade one is $2/lb
Grade two is $2.83/lb
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