Question

A store is having a sale on trail mix and jelly beans. For
2
pounds of trail mix and
3
pounds of jelly beans, the total cost is
$14
. For
6
pounds of trail mix and
5
pounds of jelly beans, the total cost is
$28
. Find the cost for each pound of trail mix and each pound of jelly beans.

Answer 1

2t + 3j = 14 ....multiply by -3
6t + 5j = 28
--------------
-6t - 9j = - 42 (result of multiplying by -3)
6t + 5j = 28
------------add
-4j = - 14
j = -14/-4
j = 3.50

2t + 3j = 14
2t + 3(3.50) = 14
2t + 10.50 = 14
2t = 14 - 10.50
2t = 3.50
t = 3.50/2
t = 1.75

so the trail mix (t) costs 1.75 per lb and the jellybeans (j) costs 3.50 per lb

Answer 2

x= cost for each pound of trail mix
y=cost for eache pound of jelly beans.

We can suggest this system of equations:
2x+3y=14
6x+5y=28

1)we solve this system by substituion method.
2x+3y=14
3y=14-2x
y=(14-2x)/3

6x+5(14-2x)/3=28
6x+(70-10x)/3=28
18x+70-10x=84
8x=84-70
8x=14
x=14/8
x=1.75

y=(14-2x)/3
y=(14-2*1.75)/3
y=(14-3.5)/3
y=10.5/3
y=3.5

Answer: the cost for each pound of trail mix is $1.75, and the cost for each pound of jelly beans is $3.5.

other method: equalization method.
2x+3y=14    ⇒x=(14-3y)/2
6x+5y=28    ⇒x=(28-5y)/6

(14-3y)/2=(28-5y)/6
least common multiple=6
3(14-3y)=(28-5y)
42-9y=28-5y
-9y+5y=28-42
-4y=-14
y=-14/-4=3.5


x=(14-3y)/2
x=(14-3*3.5)/2
x=(14-10.5)/2
x=3.5/2
x=1.75

Answer: the cost for each pound of trail mix is $1.75, and the cost for each pound of jelly beans is $3.5.