Answer:
The system of inequalities is
[tex]x+y\leq 15[/tex]
[tex]3x+5y\geq 60[/tex]
The graph in the attached figure
Step-by-step explanation:
The correct question is
Write a system of inequalities
Let
x ----> the number of hours worked mowing lawns
y ----> the number of hours worked as a babysitter
we know that
You can spend no more than 15 hours a week at your two jobs
The word "no more" means "less than or equal to"
so
[tex]x+y\leq 15[/tex] ----> inequality A
You need to earn at least $60 a week
The word "at least" means "greater than or equal to"
so
[tex]3x+5y\geq 60[/tex] ----> inequality B
Solve the system of inequalities by graphing
The solution is the triangular shaded area
see the attached figure
The situation can be represented by a system of linear inequalities.
The system of linear inequalities that represent the situation are;
Reasons:
Number of hours available each week = 15 hours
The amount made from mowing lawns = $3/hour
The amount made from babysitting = $5/hour
Amount needed per week = $60
Required:
The equation representing the word problem.
Solution:
Let x represent the time spent mowing lawns , and let y represent the time
spent babysitting, we have the following linear inequalities;
3·x + 5·y ≥ 60
x + y ≤ 15
Which gives;
x ≤ 15 - y
3 × (15 - y) + 5·y ≥ 60
45 - 3·y + 5·y ≥ 60
2·y ≥ 60 - 45 = 15
y ≥ 7.5
x ≤ 7.5
Learn more about linear inequalities here:
https://brainly.com/question/7096732
https://brainly.com/question/1757361
