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Posted by **Jamese** on Sunday, October 21, 2012 at 12:23pm.

- Math -
**Reiny**, Sunday, October 21, 2012 at 1:01pmfirst 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)

- Math -
**Shell**, Sunday, October 21, 2012 at 1:40pmdefine 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

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,

(27-6x)/5=(61-8x)/15

*15=*15

3(27-6x)=61-8x

81-18x=61-8x

+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