Question

You are buying plants and soil for your garden. The soil cost $4 per bag and the plants cost $10 each. You want to buy at least 5 plants and can spend no more than $100. Write a system of linear inequalities to model the situation.

Answer 1

The system of linear inequalities to model the situation is written as:

x + y ≥ 5..... Equation 1

4x + 10y ≤ 100..... Equation 2

Explanation:

Let

The number is soil = x

The number of plants = y

You are buying plants and soil for your garden.

You want to buy at least 5 plants

At least = greater than or equal to with the inequality sign(≥)

Hence:

x + y ≥ 5..... Equation 1

The soil cost $4 per bag and the plants cost $10 each and can spend no more than $100.

No more than means Less than or equal to with the inequality sign( ≤ )

Hence:

$4 × x +$10 × y ≤ $100

= 4x + 10y ≤ 100..... Equation 2

Therefore, the system of linear inequalities to model the situation is written as:

x + y ≥ 5..... Equation 1

4x + 10y ≤ 100..... Equation 2