Question

Glenn bought a game system and 3 video games for $375. Jim bought a game system and 4 videogames at the same store for $410.-Each game system costs the same.-Each video game costs the same.What is the cost, in dollars, of one game system?

Answer 1

To obtain the cost of one game system, the following steps are necessary:

Step 1: Let the unknown costs of a game system and a video game be represented by the variables x and y, respectively.

That is :

$\begin{gathered} x\Rightarrow\text{ cost of one game system} \\ y\Rightarrow\text{ cost of one video game} \end{gathered}$

Step 2: Transform each of the first two sentences of the question into mathematical equations, as follows:

$\begin{gathered} \text{Sentence 1:} \\ x+(3\times y)=375 \\ \text{Sentence 2:} \\ x+(4\times y)=410 \end{gathered}$

Step 3: Assign the equations numbers, and solve them simultaneously, as below:

$\begin{gathered} x+(3\times y)=375 \\ \Rightarrow x+3y=375\ldots\ldots\text{.(1)} \\ x+(4\times y)=410 \\ \Rightarrow x+4y=410\ldots\ldots\ldots(2) \\ \end{gathered}$

Now:

$\begin{gathered} \text{Subtract equation 1 from equation 2:} \\ (x+4y)-(x+3y)=410-375 \\ x+4y-x-3y=35 \\ x-x+4y-3y=35 \\ 0+y=35 \\ \Rightarrow y=35 \end{gathered}$

Finally:

$\begin{gathered} \text{substitute the value of y into equation 1 and solve for x:} \\ x+3y=375\ldots\ldots\text{.(1)} \\ \Rightarrow x+3(35)=375 \\ \Rightarrow x+105=375 \\ \Rightarrow x=375-105 \\ x=270 \end{gathered}$

Therefore the cost, in dollars, of one game system is 270