Question

Jaquez earns money by doing yard work. It takes her an average of 3 hours to pull
weeds and an average of 2.5 hours to mow the lawn. She can work no more than 8
hours a day. She charges $50 to weed and $65 to mow the lawn. She needs to cover
her expenses of $120 to make a profit. Write a system of inequalities that would help
determine how many flowerbeds and lawns he could complete on a given day. (Note -
you do not need to solve, just write the system and label the variables you use)

Answer 1

Answer:

Jaquez earns money. The system of equations are 3m + 2.5n ≤ 8 and 50m + 65n ≥ 120.

Solution:

Given, Jaquez earns money by doing yard work.  

We have to write a system of inequalities that would help determine how many flowerbeds and lawns he could complete on a given day.  

Now, let the number of flower beds he could complete on a given day be m

And the number of lawns he could complete on a day be n.

Now, it takes her an average of 3 hours to pull weeds and an average of 2.5 hours to mow the lawn.  

She can work no more than 8 hours a day.  

Then, 3 x m + 2.5 x n ≤ 8 ⇒ 3m + 2.5n ≤ 8

And, She charges $50 to weed and $65 to mow the lawn.  

She needs to cover her expenses of $120 to make a profit.  

Then, 50 x m + 65 x n ≥ 120 ⇒ 50m + 65n ≥ 120.

Hence, the system of equations are 3m + 2.5n ≤ 8 and 50m + 65n ≥ 120