A store is having a sale on jelly beans and trail mix. For 6 pounds of jelly beans and 2 pounds of trail mix, the total cost is $22. For 3 pounds of jelly beans and 5 pounds of trail mix, the total cost is $16. Find the cost for each pound of jelly beans and each pound of trail mix.

Jelly Bean price per pound = $3.25, Trail Mix price per pound = $1.25

Step-by-step explanation:

Let jb = price per pound of jelly beans

Let tm = price per pound of trail mix

equation 1 -> 6*jb + 2*tm = 22

equation 2 -> 3*jb + 5*tm = 16

simplify equation 1

6*jb + 2tm = 22

2*tm = 22 - 6*jb

divide by 2

tm = 11 - 3*jb

plug this into equation 2

3*jb + 5*tm = 16

3*jb + 5*(11-3*jb) = 16

3*jb + 55 - 15*jb = 16

-12*jb + 55 = 16

-12*jb = 16 - 55

-12*jb = -39

jb = -39/-12

jb = 3.25

then, plug the cost per pound of jelly beans back into the simplified equation 1

tm = 11 - 3*jb

tm = 11 - 3*3.25

tm = 1.25