Explanation Given Information: Peanuts and mixed nuts must be mixed to get 13 lb of mixed nuts for a wedding reception for which $ 71 has been allocated by the wedding couple for nuts with peanut costing $ 4.50 per pound and fancy nuts costing $ 7.00 per pound. Formula used: The applied problems using system of equations can be solved through the following steps: Step 1: Understand the problem. Step 2: Define variables and frame equation. Step 3: Solve the equations. Step 4: Verify the solution. Step 5: State the solution. Calculation: Consider provided information about the mixed nuts for a wedding reception. The number of pounds of peanuts and the number of pounds of fancy nuts to be mixed is required. Define the variables to the two unknown variables. x = number of pounds of peanuts y = number of pounds of fancy nuts Frame the system of equations: The total quantity of mixed nuts is 13 lb . So, the equation is: x + y = 13 …… (1) The cost of peanuts is $ 4.50 per pound and the cost of fancy nuts is $ 7.00 per pound and the total amount allotted is $ 71 . So, another equation is: 4.50 x + 7 y = 71 …… (2) The system of two equations is: x + y = 13 And, 4.50 x + 7 y = 71 Solve the system of equations. In the provided system of equations, use the equation ( 1 ) and solve for y . So this would make it easier to substitute this into another equation and solve by substitution method. x + y = 13 Subtract x from both the sides of the equation. x + y − x = 13 − x y = 13 − x Now, substitute y = 13 − x in equation ( 2 ) . So, the equation becomes, 4.50 x + 7 ( 13 − x ) = 71 Use the distributive property a ( b + c ) = a b + a c to clear the parenthesis

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Author: BITTINGER

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Chapter 13, Problem 27RE

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To calculate: The number of pounds of peanuts and number of pounds of fancy nuts that must be mixed to get 13 lb of mixed nuts for a wedding reception for which $71 has been allocated by the wedding couple for nuts with peanut costing $4.50 per pound and fancy nuts costing $7.00 per pound.

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Ch. 13.1 - Prob. 1SR Ch. 13.1 - Prob. 2SR Ch. 13.1 - Prob. 1DE Ch. 13.1 - Prob. 2DE Ch. 13.1 - Prob. 3DE Ch. 13.1 - Prob. 4DE Ch. 13.1 - Prob. 5DE Ch. 13.1 - Prob. 6DE Ch. 13.1 - Prob. 7DE Ch. 13.1 - Prob. 8DE

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The number of pounds of peanuts and number of pounds of fancy nuts that must be mixed to get 13 lb of mixed nuts for a wedding reception for which $ 71 has been allocated by the wedding couple for nuts with peanut costing $ 4.50 per pound and fancy nuts costing $ 7.00 per pound.

Solution Summary: The author calculates the number of pounds of peanuts and fancy nuts that must be mixed for a wedding reception for which 71 has been allocated.

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To calculate: The number of pounds of peanuts and number of pounds of fancy nuts that must be mixed to get 13 lb of mixed nuts for a wedding reception for which $71 has been allocated by the wedding couple for nuts with peanut costing $4.50 per pound and fancy nuts costing $7.00 per pound.

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