Q53. - Algebra 2

Question

53. CAMERA SUPPLIES Mrs. Franklin is planning a family vacation. She bought 8 rolls of film and 2 camera batteries for 23 . The next day, her daughter went back and bought 6 more rolls of film and 2 batteries for her camera. This bill was 18 . State the price of a roll of film and a camera battery.

Step-by-Step Solution

Answer

The price of a roll of film is 2.5 . 

 The price of a camera battery is 1.5 .

Step 1 - State the definition of a matrix.

A rectangular array of numbers arranged in rows and columns is called a matrix.

Step 2 - Obtain the equations.

Let, the price of a roll of film be  x and the price of a camera battery be y . The information that Mrs. Franklin bought 8 rolls of film and 2 batteries for23  . This can be written using x  and  y as:

$8x+2y=23$

As price of one roll of film is x , then cost of 8 rolls is  8x. Similarly, price of 1 battery is y , then price of 2 batteries is 2y . Adding all the quantities gives 23 .

 Now, Mrs. Franklin’s daughter bought 6 rolls of film and 2 batteries for 18 . This can be written using  x and  y as:$6x+2y=18$

Since price of one roll of film is x , then cost of 6 rolls is 6x . Similarly, price of 1 battery is y , then price of 2 batteries is 2y . Adding all the quantities gives 18 .

 Then, the two equations formed are:$8x+2y=23$  (1)

$6x+2y=18$    (2)

Step 3 - Solve the equations.

Solve the equations using substitution.

 Solve equation 2 as:$\begin{array}{c}6x+2y=18\\ 6x+2y-6x=18-6x\\ 2y=18-6x\\ \frac{2y}{2}=\frac{18}{2}-\frac{6x}{2}\\ y=9-3x\end{array}$

Substitute  y with $y=9-3x$  in equation 1:

$\begin{array}{c}8x+2y=23\\ 8x+2(9-3x)=23\\ 8x+18-6x=23\\ 2x+18-18=23-18\\ 2x=5\\ x=2.5\end{array}$

Now, put the value of x  in equation 2:

$\begin{array}{c}6x+2y=18\\ 6\times 2.5+2y=18\\ 15+2y=18\\ 15+2y-15=18-15\end{array}$

That implies,

$\begin{array}{c}2y=3\\ \frac{2y}{2}=\frac{3}{2}\\ y=1.5\end{array}$

Step 4 - State the conclusion.

Here, $x=2.5$ ,  and $y=1.5$ . 

 Therefore price of a roll of film is $x=2.5$  that is $2.5$  and price of a camera battery is $y=1.5$  that is  $1.5$