<u>Answer-</u>
The equation is
and Julianne will begin making a profit after 168 days.
<u>Solution-</u>
Julianne's start-up cost = $52,000,
Each day, she spends = $650,
and she earns = $960 per day,
If 'd' is the number of days to overcome the start-up and daily operation cost, then
total operation cost of d days = $650d and
total student lesson fees earned in d days = $960d
∴ The equation to represent the situation is,
![960d-650d = 52000](https://tex.z-dn.net/?f=960d-650d%20%3D%2052000)
∴ Julianne will begin making a profit,
![\Rightarrow 960d-650d \geq 52000](https://tex.z-dn.net/?f=%5CRightarrow%20960d-650d%20%5Cgeq%2052000)
![\Rightarrow 310d \geq 52000](https://tex.z-dn.net/?f=%5CRightarrow%20310d%20%5Cgeq%2052000)
![\Rightarrow d \geq \frac{52000}{310} =167.74 \approx168(ans)](https://tex.z-dn.net/?f=%5CRightarrow%20d%20%5Cgeq%20%5Cfrac%7B52000%7D%7B310%7D%20%3D167.74%20%5Capprox168%28ans%29)