Question

Question 3

1 pts
A student has started a lawn care business. He charges $15 per hour to mow lawns and 20 per hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per week. His goal is to make at least $300 per week.
Which two inequalities below could be used in a system of inequalities to solve this problem? x= # of hours lawn mowing AND y=# of hours gardening
x+y ≤ 20
20 x+20 y ≥300
x+y ≥20
20 x+20 y ≤300
15 x+20 y ≤ 300
15 x+20 y ≥300

Answer 1

First choice: x + y ≤ 20

and

last choice: 15x + 20y ≥ 300

Explanation:

If x is the number of hours spent mowing and y the number of hours spent gardening, total numbers that the student spends in a week is

x + y

However, this cannot exceed(at most) 20 hours. So this is a ≤ inequality:

x + y ≤ 20

Amount of money the student makes with this amount of work is
15x + 20y

The student wants to earn at least $300

This implies a ≥ inequality

So the second equation is

15x + 20y ≥ 300

You should be careful of the wordings in these types of questions.
at most implies ≤

at least implies ≥