Question

Marsha is buying plants and soil for her garden. The soil cost $4 per

bag, and the plants cost $10 each. She wants 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

p ≥ 5

4s + 10p ≤ 100

Explanation:

Here, we want to write a system of inequalities

Let the number of bags of soil be s and the number of plants be p

She wants to buy at least 5 plants

mathematically, when something is at least 5, it means greater than or equal to 5

In inequality, we have this as;

p ≥ 5

Secondly, she wants to spend not more than $100; she can spend less but cannot spend more

We have this as;

The number of bags she can buy at $4 per bag is 4 * s = 4s

the number of plants at $10 per one will be;

10 * p = 10p

Adding both should give a cost less than or equal to 100

We have this as;

4s + 10p ≤ 100

So, we have the system of inequalities as;

p ≥ 5

4s + 10p ≤ 100