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Q4.

Expert-verifiedFound in: Page 396

Book edition
Student Edition

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

Pages
801 pages

ISBN
9780078884801

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

** **

**F$\mathbf{\$}\mathbf{45}$ G****$\mathbf{\$}\mathbf{59}$ H$\mathbf{\$}\mathbf{108}$ J $\mathbf{\$}\mathbf{119}$**

The price of an **electric bill is option F$\mathbf{\$}\mathbf{45}$.**

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

$\begin{array}{l}ax+by=p\\ cx+dy=q\end{array}$

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.

Assume the price of 1 table saw to be $\u2018\$x\u2019$ and the price of 1 electric drill to be $\u2018\$y\u2019$.

Price of 1 table saw is $\$x$*.*

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

Price of 1 electric drill is $\$y$.

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

From the ${1}^{st}$ condition,

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

$4x+9y=881\text{\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\dots \left(1\right)$

From the ${2}^{nd}$ condition,

The receipts from the saws exceeded the receipts from the drills by $\$71$. $x=y+71\text{\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\dots \left(2\right)$

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 $x=y+71\text{\hspace{0.17em}}$ in equation $4x+9y=881$ to get the value of $\u2018y\u2019$which is the price of electric drill.

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

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

Therefore, option $F\$45$ is correct.

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