Martha is planting a garden that will cover up to 400 square feet. She wants to plant two types of flowers, daises and roses. Each daisy covers 2 square feet and each rose covers 1.5 square feet. Daises cost $2 a piece and each rose costs $3 a piece. Martha doesn't want to spend over $500 on her garden

150 daisies and 66 roses.

Step-by-step explanation:

To carry out the exercise, you have to propose equations with the requirements of Martha, a garden of 400 square feet and not spend more than $ 500. Let X be the number of daisies and Y the number of roses. We have left that:

2 * X + 1.5 * Y = 400 (1)

2 * X + 3 * Y = 500 (2)

We have two equations with two unknowns, therefore we proceed to solve. If we subtract (1) in (2) we have:

2 * X + 3 * Y - 2 * X - 1.5 * Y = 500 - 400, rearranging we have:

1.5 * Y = 100

Y = 100 / 1.5 = 66.7, it would be approximately 66 roses.

Replacing the value of Y now in (1) we have:

2 * X + 1.5 * 66.7 = 400

2 * X + 99.9 = 400

X = (400-99.9) / 2 = 150.05, would be approximately 150 daisies.

We replace in (1) and (2) to check:

2 * 150 + 1.5 * 66 = 399, is the maximum we can spend because one more flower would be spent.

2 * 150 + 3 * 66 = 498, is the maximum we can spend because one more flower would be spent.

Therefore it meets Martha's requirements for his garden, 150 daisies and 66 roses.