Jules has $1200 and is spending $30 per week.
We can express the amount of money Jules is having in x weeks as:
![M_J=1200-30x](https://img.qammunity.org/2023/formulas/mathematics/college/x1yf41ed9s8z8ptrikf8ek02ecdbuhtwvv.png)
(See that 30 is expressed in negative because it reduces the amount of money with increasing x).
Kelsey has $400 and is saving $50 per week. This can be written as:
![M_K=400+50x](https://img.qammunity.org/2023/formulas/mathematics/college/wduznwkvl4a1myr6mpp4yo9y13g9jxz30f.png)
Then, we can write Mj=Mk to calculate in which week it happens that they have the same amount of money:
![\begin{gathered} M_J=M_K \\ 1200-30x=400+50x \\ 1200-400=50x+30x \\ 800=80x \\ x=(800)/(80) \\ x=10 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/d1a6kf3rlrzclfporsacldarhp9w48qtbn.png)
I happens when x=10 weeks. The answer is 10.