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: 8220106960455

Author: CARMAN

Publisher: PEARSON

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 11.1, Problem 5CE

To determine

To find: The cost of a leather cleaner bottle and protectant bottle.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.1, Problem 4CE

Chapter 11.1, Problem 6CE

Students have asked these similar questions

(1) Write the following quadratic equation in terms of the vertex coordinates.

No chatgpt pls will upvote Already got wrong chatgpt answer

data management Q7

Chapter 11 Solutions

EBK MATHEMATICS FOR THE TRADES

Ch. 11.1 - Simplify: 2(3 + 2y) 3y Ch. 11.1 - Prob. 2LC Ch. 11.1 - Solve each of the following systems of equations...Ch. 11.1 - Solve each of the following systems of equations...Ch. 11.1 - Solve each of the following systems of equations...Ch. 11.1 - Solve each of the following systems of equations...Ch. 11.1 - Prob. 5AE Ch. 11.1 - Solve each of the following systems of equations...Ch. 11.1 - Prob. 7AE Ch. 11.1 - Solve each of the following systems of equations...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

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.

Concept explainers

Videos

To find: The cost of a leather cleaner bottle and protectant bottle.

Want to see the full answer?

Chapter 11 Solutions