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 $20. For 3 pounds of jelly beans and 5 pounds of trail mix, the total cost is $23. Find the cost for each pound of jelly beans and each pound of trail mix.

Jelly beans are $2.25/pound, trail mix $3,25/pound

Step-by-step explanation:

Let's say that the cost of a pound of jelly beans is x, and that the cost of a pound of trail mix is y.

We can then say that 6 pounds of jelly beans + 2 pounds of trail mix, or 6x+2y, equals 20.

Next, 3x+5y=23, and we have

6x+2y=20

3x+5y=23

We can multiply the whole second equation by - 2 and add it to the first one to get rid of the x, so - 8y=-26. Divide both sides by - 8, and a pound of trail mix, or y, is 26/8, or $3.25. Plugging this back into the first equation, we get that

6x+2 (26/8) = 20, so (20-2 (26/8)) / 6=x=2.25, or the cost of one pound of jelly beans