Systems of Equations and Matrices
Solving a word problem using a system of linear equations of the form Ax...
A store is having a sale on jelly beans and almonds. For 6 pounds of jelly beans and 2 pounds of almonds, the total cost is $\$ 22$. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $\$ 16$. Find the cost for each pound of jelly beans and each pound of almonds.
Cost for each pound of jelly beans: $\$ \square$
Cost for each pound of almonds: $s \square$

Step 1 ：Let's denote the cost of each pound of jelly beans as 'j' and the cost of each pound of almonds as 'a'.

Step 2 ：From the problem, we can form two equations: \(6j + 2a = 22\) and \(3j + 5a = 16\).

Step 3 ：We can solve this system of equations to find the values of 'j' and 'a'.

Step 4 ：The solution to the system of equations gives the cost of each pound of jelly beans and almonds.

Step 5 ：The cost of each pound of jelly beans is \(\frac{13}{4}\) dollars and the cost of each pound of almonds is \(\frac{5}{4}\) dollars.

Step 6 ：Final Answer: Cost for each pound of jelly beans: \(\boxed{\$ 3.25}\), Cost for each pound of almonds: \(\boxed{\$ 1.25}\)