Problem

Directions: Define your variables and set up a system of equations, then solve.
9. A storeowner mixed 8 pounds of peanuts and 5 pounds of M\&M's. This 13 pound mixture sold for $\$ 55.27$. A second mixture included 6 pounds of peanuts and 4 pounds of M\&M's. This 10 pound mixture sold for $\$ 42.70$. Find the cost per pound of the peanuts and M\&M's.

Answer

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Answer

Final Answer: \(\boxed{(\$3.79, \$4.99)}\).

Steps

Step 1 :Define the cost per pound of peanuts as 'p' and the cost per pound of M&M's as 'm'.

Step 2 :Set up the first equation from the first mixture: \(8p + 5m = 55.27\).

Step 3 :Set up the second equation from the second mixture: \(6p + 4m = 42.70\).

Step 4 :Solve the system of equations to find the values of 'p' and 'm'.

Step 5 :The solution is {m: 4.99000000000000, p: 3.79000000000000}.

Step 6 :The cost per pound of peanuts is \$3.79 and the cost per pound of M&M's is \$4.99.

Step 7 :Final Answer: \(\boxed{(\$3.79, \$4.99)}\).

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