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Q4.

Expert-verified

Algebra 1

Found in: Page 396

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

A home goods store received $$ 881$ from the sale of 4 table saws and 9 electric drills. If the receipts from the saws exceeded the receipts from the drills by $$ 71$ , what is the price of an electric drill?

F $$ 45$ G $$ 59$ H $$ 108$ J $$ 119$

The price of an electric bill is option F $$ 45$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. State the concept of Linear System with two variables.

A linear system of two equations with two variables is any system that can be written in the form.

$\begin{array}{l} a x + b y = p \\ c x + d y = q \end{array}$

Where any of the constants can be zero with the exception that each equation must have at least one variable in it.

Also, the system is called linear if the variables are only to the first power, are only in the numerator and there are no products of variables in any of the equations.

Step 2. Write the equations from the conditions given in the question.

Assume the price of 1 table saw to be $‘ $ x ’$ and the price of 1 electric drill to be $‘ $ y ’$ .

Price of 1 table saw is $$ x$ .

$\begin{array}{r} Therefore, price of 4 table saws = 4 \times x \\ = $ 4 x \end{array}$

Price of 1 electric drill is $$ y$ .

$\begin{array}{r} Therefore, price of 9 electric drill = 9 \times y \\ = $ 9 y \end{array}$

From the $1^{s t}$ condition,

A home goods store received $$ 881$ from the sale of 4 table saws and 9 electric drills.

$4 x + 9 y = 881 \dots (1)$

From the $2^{n d}$ condition,

The receipts from the saws exceeded the receipts from the drills by $$ 71$ . $x = y + 71 \dots (2)$

Step 3. Solve the above system of equations by substitution method.

Substitution method: The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equation gets transformed into one linear equation with only one variable, which can then easily be solved.

Substitute $x = y + 71$ in equation $4 x + 9 y = 881$ to get the value of $‘ y ’$ which is the price of electric drill.

$\begin{matrix} 4 x + 9 y = 881 \\ 4 (y + 71) + 9 y = 881 \\ 4 y + 284 + 9 y = 881 \\ 4 y + 9 y + 284 = 881 \\ 13 y + 284 = 881 \\ 13 y = 881 - 284 \\ 13 y = 597 \\ \frac{13 y}{13} = \frac{597}{13} \\ y = 45.92 \end{matrix}$

Therefore, the price of an electric bill is $$ 45.92$ .

Therefore, option $F $ 45$ is correct.

Most popular questions for Math Textbooks

Determine the best method to solve each system of equations. Then solve the system.

$\begin{array}{l} 3 x + 4 y = 26 \\ 2 x + 3 y = 19 \end{array}$

Solve each equation or formula for the variable specified.

$2 x + 4 y = 12$ , for x

Graph each system and determine the number of solutions that it has. If it has one solution, name it.

$\begin{array}{l} 3 x + y = 5 \\ 6 x = 10 - 2 y \end{array}$

Use substitution to solve each system of equations.

$y = - 2 x - 3 x + y = 9$

Use elimination to solve each system of equations.

$\begin{matrix} 9 x - 24 y = - 6 \\ 3 x + 4 y = 10 \end{matrix}$

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