Given:
Christopher has 20 video games and will buy 4 more each month
Peter has 92 video games and will sell 5 each month
Let the number of months required for them to have an equal number of video games be x
Hence:
[tex]\begin{gathered} 20\text{ + 4}\times\text{ x = 92 - 5}\times x \\ 20\text{ + 4x = 92 -5x} \end{gathered}[/tex]
Solving for x:
[tex]\begin{gathered} \text{Collect like terms} \\ 4x\text{ + 5x = 92 - 20} \\ 9x\text{ = 72} \\ \text{Divide both sides by 9} \\ \frac{9x}{9}\text{ = }\frac{72}{9} \\ \text{x = 8} \end{gathered}[/tex]
The number of video games they would both have is obtained by substitution
[tex]\begin{gathered} =\text{ 20 + 4x} \\ =\text{ 20 + 4}\times8 \\ =\text{ 20 + 32} \\ =\text{ 52} \end{gathered}[/tex]
Answer:
8 months , 52 video games
