Answer:
The cost of Jelly Beans = ![$ \frac{5}{4} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B5%7D%7B4%7D%20%24)
The cost of Trail Mix = ![$ \frac{9}{4} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B9%7D%7B4%7D%20%24)
Step-by-step explanation:
Given the cost of 6 pounds of Jelly Beans and 2 pounds of trail mix is $12.
Also, the cost of 3 pounds of Jelly Beans and 5 pounds of Trail mix is $15.
Call the cost of one pound of Jelly beans as J
And cost of one pound of Trail Mix as T.
Now, converting the given data to mathematical form, we would have:
![$ 6J + 2T = 12 $](https://tex.z-dn.net/?f=%24%206J%20%2B%202T%20%3D%2012%20%20%24)
Dividing through out by 2 we have:
![$ 3J + T = 6 \hspace{15mm} .....(1) $](https://tex.z-dn.net/?f=%24%203J%20%2B%20T%20%3D%206%20%5Chspace%7B15mm%7D%20%20.....%281%29%20%24)
![$ 3J + 5T = 15 \hspace{15mm} ....(2) $](https://tex.z-dn.net/?f=%24%203J%20%2B%205T%20%3D%2015%20%5Chspace%7B15mm%7D%20....%282%29%20%24)
To solve (1) and (2), subtract the two equations which will give us:
![$ -4T = - 9 $](https://tex.z-dn.net/?f=%24%20-4T%20%3D%20-%209%20%24)
⇒ T = 9/4
Substituting the value of T in (1), we have:
![$ 3J = 6 - \frac{9}{4} $](https://tex.z-dn.net/?f=%24%203J%20%3D%206%20-%20%5Cfrac%7B9%7D%7B4%7D%20%24)
![$ \implies 3J = \frac{24 - 9}{4} = \frac{(3)(8 - 3)}{4} = \frac{5}{4} $](https://tex.z-dn.net/?f=%24%20%5Cimplies%203J%20%3D%20%5Cfrac%7B24%20-%209%7D%7B4%7D%20%3D%20%5Cfrac%7B%283%29%288%20-%203%29%7D%7B4%7D%20%3D%20%5Cfrac%7B5%7D%7B4%7D%20%24)
∴ J = 5/4