Answer:
The cost of Jelly Beans = [tex]$ \frac{5}{4} $[/tex]
The cost of Trail Mix = [tex]$ \frac{9}{4} $[/tex]
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 $15.
Call the cost of one pound of Jelly beans as J
And cost of one pound of Trail Mix as T.
Now, converting the given data to mathematical form, we would have:
[tex]$ 6J + 2T = 12 $[/tex]
Dividing through out by 2 we have:
[tex]$ 3J + T = 6 \hspace{15mm} .....(1) $[/tex]
[tex]$ 3J + 5T = 15 \hspace{15mm} ....(2) $[/tex]
To solve (1) and (2), subtract the two equations which will give us:
[tex]$ -4T = - 9 $[/tex]
⇒ T = 9/4
Substituting the value of T in (1), we have:
[tex]$ 3J = 6 - \frac{9}{4} $[/tex]
[tex]$ \implies 3J = \frac{24 - 9}{4} = \frac{(3)(8 - 3)}{4} = \frac{5}{4} $[/tex]
∴ J = 5/4
