Answer:
Greatest number of people they may invite within their budgeted
![x=131](https://img.qammunity.org/2021/formulas/business/high-school/lc4343jitqowpbz7vlejzuupgq5qfmm1wn.png)
Step-by-step explanation:
Given,
Clean up charges
![=\$ 50](https://img.qammunity.org/2021/formulas/business/high-school/sir3yxtx4m9xj9g8yz5bl9q0th3aqgbazz.png)
Per person charges
![=\$ 30](https://img.qammunity.org/2021/formulas/business/high-school/16pwctun0vrpnp52dog2wqpmzowogsls8j.png)
Solution
Let the number of people they may invite is
![x](https://img.qammunity.org/2021/formulas/mathematics/middle-school/p9sq9b3rc5nwoqzhzc8wcaj51b36281l9g.png)
![\$ 30* x+\$ 50=\$ 4000](https://img.qammunity.org/2021/formulas/business/high-school/hbue6uerocvfo1uh86j83b4w1h7iq738bo.png)
![\$ 30* x=\$ 4000-\$ 50](https://img.qammunity.org/2021/formulas/business/high-school/mczhjsgu6ts3m9pv2b7yph4jfckrhsmt81.png)
![30* x=3950](https://img.qammunity.org/2021/formulas/business/high-school/sel7n5j27gddxmm72sxihpkfdfm8aerq93.png)
![x=3950/30](https://img.qammunity.org/2021/formulas/business/high-school/r8svn3r3rra4jc98ccyixrupb6tl4qc7kv.png)
![x=131.666](https://img.qammunity.org/2021/formulas/business/high-school/ju2beodhzhk0stw2lewoj2ahi4k7orusrt.png)
Maximum number of people they may invite within their budgeted
![x=131](https://img.qammunity.org/2021/formulas/business/high-school/lc4343jitqowpbz7vlejzuupgq5qfmm1wn.png)