  ### Home > GC > Chapter 2 > Lesson 2.3.1 > Problem2-104

2-104. Berti is the Shape Factory’s top employee. She has received awards every month for having the top sales figures so far for the year. If she stays on top, she will receive a $\5000$ bonus for excellence. She currently has sold $16,250$ shapes and continues to sell $340$ per month.

Since there are eight months left in the sales year, Sarita is working hard to catch up. While she has only sold $8,830$ shapes, she is working overtime and on weekends so that she can sell $1,082$ per month. Will Sarita catch up with Berti before the end of the sales year? If so, when?

 month $\$ Berti: $4$ $16,250$ ${\color{blue}{\Big)}} +340$ From month 4 to month 5 Berti gained $340.${\color{blue}{\Big)}} +340$ From month 5 to month 6 Berti gained$340. $5$ $6$ $7$ $8$ $...$ $...$ $12$ $\uparrow$end of year

 month $\$ Sarita: $4$ $8830$ ${\color{blue}{\Big)}} +1082$ From month 4 to month 5 Sarita gained $1082.${\color{blue}{\Big)}} +1082$ From month 5 to month 6 Sarita gained$1082. $5$ $6$ $7$ $8$ $...$ $...$ $12$ $\uparrow$end of year

Write a system of equations and use substitution to solve.
Berti's equation will be $y=340x+16,250$.
What will Sarita's equation be?