Answer:
![25x+15y\geq 1975\\y\leq 4x\\y\geq 50\\x\geq 0](https://tex.z-dn.net/?f=25x%2B15y%5Cgeq%201975%5C%5Cy%5Cleq%204x%5C%5Cy%5Cgeq%2050%5C%5Cx%5Cgeq%200)
Step-by-step explanation:
Let x represents the number of lawns mowed by Mike and y represents the number of cars washed by Beth.
Then, the amount earned by Mike if he charges $25 for moving the lawn![=25x](https://tex.z-dn.net/?f=%3D25x)
And the amount earned by Beth if she charges $15 for moving the lawn![=15x](https://tex.z-dn.net/?f=%3D15x)
Then, as need at least $1975 in order to go Disneyworld.
So, first inequality is,
![25x+15y\geq 1975](https://tex.z-dn.net/?f=25x%2B15y%5Cgeq%201975)
Now, it is given that the number of cars that Beth wash is no more than four times the number of lawns Mike has scheduled to mow. So, this gives the inequality,
![y\leq 4x](https://tex.z-dn.net/?f=y%5Cleq%204x)
Next, it is given that Beth will wash at least 50 cars. So,
![y\geq 50](https://tex.z-dn.net/?f=y%5Cgeq%2050)
Lastly, as the number of lawns mowed can't be negative, so
![x\geq 0](https://tex.z-dn.net/?f=x%5Cgeq%200)