The cost of each pound of jelly beans is $ 2.25 and cost of each pound of almond is $ 1.25
<em><u>Solution:</u></em>
Let the cost of each pound of jelly beans is "a"
Let the cost of each pound of almond is "b"
<em><u>For 6 pounds of jelly beans and 2 pounds of almonds, the total cost is $16</u></em>
Therefore, we frame a equation as:
6 pounds of jelly beans x cost of each pound of jelly beans + 2 pounds of almonds x cost of each pound of almond = 16
![6 \times a + 2 \times b = 16](https://tex.z-dn.net/?f=6%20%5Ctimes%20a%20%2B%202%20%5Ctimes%20b%20%3D%2016)
6a + 2b = 16 --------- eqn 1
<em><u>For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $13</u></em>
Therefore, we frame a equation as:
3 pounds of jelly beans x cost of each pound of jelly beans + 5 pounds of almonds x cost of each pound of almond = 13
![3 \times a + 5 \times b = 13](https://tex.z-dn.net/?f=3%20%5Ctimes%20a%20%2B%205%20%5Ctimes%20b%20%3D%2013)
3a + 5b = 13 ----------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Multiply eqn 2 with 2</u></em>
6a + 10b = 26 --------- eqn 3
<em><u>Subtract eqn 1 from eqn 3</u></em>
6a + 10b = 26
6a + 2b = 16
( - ) -------------------------
8b = 10
![b = \frac{10}{8} = 1.25](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B10%7D%7B8%7D%20%3D%201.25)
<h3>b = 1.25</h3>
<em><u>Substitute b = 1.25 in eqn 1</u></em>
6a + 2(1.25) = 16
6a + 2.5 = 16
6a = 13.5
<h3>a = 2.25</h3>
Thus cost of each pound of jelly beans is $ 2.25 and cost of each pound of almond is $ 1.25