Let x be the number of weeks after Mohammed started to save up. Since he receives $100 every week, then, after x weeks, he would receive 100x dollars.
Since he already had $50 at the beginning, then, the total amount of money y that he has saved after x weeks, is:
[tex]y=100x+50[/tex]Since the cost of the PS5 is $610, then, set y=610 and solve for x to find the number of weeks that he will need to save money:
[tex]\begin{gathered} y=610 \\ \Rightarrow610=100x+50 \\ \Rightarrow610-50=100x \\ \Rightarrow560=100x \\ \Rightarrow\frac{560}{100}=x \\ \Rightarrow x=5.6 \end{gathered}[/tex]He will need to save for at least 5.6 weeks. Nevertheless, he only receives money once a week and 5 weeks won't be enough for buying the PS5. Then, he needs to save for 6 weeks.