Mathematics, 09.12.2019 07:31, hanny13

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 than $100.

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answered: arigar

Part a) The system of linear inequalities is

$y\geq 5$

$4x+10y\leq 100$

Part b) The graph in the attached figure

Part c) A solution could be (5,7) (see the explanation)

Step-by-step explanation:

The complete question is

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 than $100

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"

$y\geq 5$ ----> inequality A

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

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

Part b) Graph the system of linear inequalities

we have

$y\geq 5$ ----> inequality A

$4x+10y\leq 100$ ----> 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

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

$7\geq 5$ ----> is true

The ordered pair (5,7) satisfy inequality A

Verify inequality B

$4(5)+10(7)\leq 100$

$90\leq 100$ ---> is true

The ordered pair (5,7) satisfy inequality B

therefore

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

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You are buying plants and soil for your garden. the soil cost 4.00 dollars per bag and the plants co...