13. You are buying plants and soil for your garden. The soil costs $4.00 per bag and the plants cost $10.00 each. You want to buy at least 5 plants and can spend no more than $100.00 total

You are buying plants and soil for your garden. The soil cost 4.00 dollars per bag and the plants cost 10.00 each. You want to buy at least 5 plants and can spend no more than10.00each.Youwanttobuyatleast5plantsandcanspendnomorethan100

a) write a system of linear inequalities to model the situation

b) Graph the system of linear inequalities

c) Identify and interpret a solution to the system

Part a) write a system of linear inequalities to model the situation

Let

x -----> the number of bags of soil

y ----> number of plants

we know that

The word "at least" means "greater than or equal"

y\geq 5y≥5 ----> inequality A

The word "no more" means "less than or equal"

4x+10y\leq 1004x+10y≤100 ----> inequality B

Part b) Graph the system of linear inequalities

we have

y\geq 5y≥5 ----> inequality A

4x+10y\leq 1004x+10y≤100 ----> inequality B

using a graphing tool

the solution is the triangular shaded area

see the attached figure

Part c) Identify and interpret a solution to the system

we know that

If a ordered pair is a solution to the system, then the ordered pair must lie on the shaded area of the solution

i take the point (5,7)

the point (5,7) lie on the shaded area of the solution

so

is a solution of the system

That means ----> You are buying 5 bags of soil and 7 plants for your garden

Verify the solution

Remember

If a ordered pair is a solution to the system, then the ordered pair must satisfy both inequalities

Verify inequality A

7\geq 57≥5 ----> is true

so

The ordered pair (5,7) satisfy inequality A

Verify inequality B

4(5)+10(7)\leq 1004(5)+10(7)≤100

90\leq 10090≤100 ---> is true

so

The ordered pair (5,7) satisfy inequality B

therefore

The ordered pair (5,7) is a solution to the system