Answer:
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.
