SOLUTION: If I buy 3 pounds of jelly beans and 8 pounds of trail mix it costs $23.00 but if i buy 5 pounds of jelly beans and 2 pounds of trail mix it costs $10.00 how much do jelly beans an

Question 1012424: If I buy 3 pounds of jelly beans and 8 pounds of trail mix it costs $23.00 but if i buy 5 pounds of jelly beans and 2 pounds of trail mix it costs $10.00 how much do jelly beans and trail mix cost on their own per pound?
Found 2 solutions by macston, fractalier:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
J=cost of jelly beans; T=cost of trail mix
.
3J+8T=$23.00
5J+2T=$10.00 . Multiply this by 4
20J+8T=$40.00 . Subtract this from first equation.
-17J=-$17.00
J=$1.00
ANSWER 1: Jelly Beans cost $1.00/pound.
.
3J+8T=$23.00
3($1)+8T=$23.00
$3+8T=$23.00
8T=$20.00
T=$2.50
ANSWER 2: Trail mix costs $2.50/pound.
.
CHECK:
5J+2T=$10
5($1)+2($2.50)=$10
$5+$5=$10
$10=$10

Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the cost of a pound of jelly beans, j.
Call the cost of a pound of trail mix, t.
Then we can write two equations...we will work in cents...
3j + 8t = 2300
5j + 2t = 1000
Let us multiply the bottom one by four and subtract it from the top one...
3j + 8t = 2300
-(20j + 8t = 4000)
--------------------
-17j = -1700
j = 100 ($1.00 a pound for jelly beans)
Now plug that in to the first equation and get
3(100) + 8t = 2300
300 + 8t = 2300
8t = 2000
t = 250 ($2.50 a pound for trail mix)
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