It is the end of the semester, and the clubs at school are recording their profits. The Science Club started out with $\$20$ and has increased its balance by an average of $\$10$ per week. The Math Club has saved $\$5$ per week after starting out with $\$50$ at the beginning of the semester.

1. Create an equation for each club. Let $x$ represent the number of weeks and $y$ represent the balance of the club’s account.

   Hint (a):

   Review your work from the problems in this lesson.

   Answer (a):

   Science Club: $y=20+10x$
   Now write an equation for the Math Club.

2. Graph both lines on one set of axes. When do the clubs have the same balance?

   Hint (b):

   Where do the lines intersect?

3. What is the balance at that point?

   Hint (c):

   What is the $y$-value of the intersection point?