Explanation Given: The cost of four bottles of leather cleaner and three bottles of protectant is $64 and cost of three bottles of leather cleaner and four bottles of protectant is $62. Procedure used: Solving linear systems by Addition: (1) If necessary, rewrite both equation in the form of A x + B y = C . (2) If necessary, multiply either equation or both equation by appropriate nonzero numbers so that the sum of the x- coefficient or the sum of the y- coefficients is 0. (3) Add the equation in step 2. The sum is an equation in one variable. (4) Solve the equation in one variable. (5) Back-substitute the value found in step 4 either of the given equations and solve for the other variable. (6) Check the solution in either of the original equations. Calculation: Consider x and y as the cost of leather cleaner bottle and protectant bottle. Here the cost of 4 bottles of leather cleaner is 4 x and cost of 3 bottles of protectant is 3 y . The sum of 4 bottles of leather cleaner and 3 bottles of protectant is $64. 4 x + 3 y = 64 (1) And the cost of 3 bottles of leather cleaner is 3 x and cost of 4 bottles of protectant is 4 y . The sum of 3 bottles of leather cleaner and 4 bottles of protectant is $62. 3 x + 4 y = 62 (2) By using the above procedure, solve the system of equations. Step 1: Eliminate the term x. Consider the x term in each equation that are 4 x and 3 x . To eliminate x , multiply each term of the equation (1) by 3. That is, 12 x + 9 y = 192 . (3) Similarly multiply each term of the equation (2) by –4. That is, − 12 x − 16 y = − 248 . (4) Step 3: Now add the equation (3) and (4) as follows. 12 x + 9 y = 192 − 12 x − 16 y = − 248 _ 0 x − 7 y = − 56 Step 4: Solve the above equation

11th Edition

ISBN: 9780134758817

Author: SAUNDERS

Publisher: PEARSON CO

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Chapter 11.1, Problem 5CE

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The cost of a leather cleaner bottle and protectant bottle.

Solution Summary: The author calculates the cost of a leather cleaner bottle and protectant bottle by adding x and y to the equations.

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