Question

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

F$\mathbf{\backslash (}\mathbf{45}$ G$\mathbf{\backslash )}\mathbf{59}$ H$\mathbf{\backslash (}\mathbf{108}$ J $\mathbf{\backslash )}\mathbf{119}$

Short answer

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

Step-by-step solution

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.

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

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.

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 $\$x$.

$\begin{array}{r}\text{Therefore,priceof4tablesaws}=4\times x\\ =\$4x\end{array}$

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

$\begin{array}{r}\text{Therefore,priceof9electricdrill}=9\times y\\ =\$9y\end{array}$

From the $1^{st}$condition,

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

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

From the $2^{nd}$condition,

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

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

Substitution method:Thesubstitution 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 $4x+9y=881$to get the value of $‘y’$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.