Question

Danielle and Maria each improved their yards by planting daylilies and ornamental grass. They bought their supplies from the same store. Danielle spent $120 on 8 daylilies and 12 bunches of ornamental grass. Maria spent $38 on 2 daylilies and 7 bunches of ornamental grass. What is the cost of one daylily and the cost of one bunch of ornamental grass?

a) Daylily: $4, Ornamental grass: $5
b) Daylily: $3, Ornamental grass: $2
c) Daylily: $5, Ornamental grass: $4
d) Daylily: $2, Ornamental grass: $3

Answer 1

To find the cost of one daylily and one bunch of ornamental grass, we can set up a system of equations using the information given. By solving the system, we find that the cost of one daylily is $12 and the cost of one bunch of ornamental grass is $2.

Step-by-step explanation:

To find the cost of one daylily and one bunch of ornamental grass, we can set up a system of equations using the information given:

Let x be the cost of one daylily and y be the cost of one bunch of ornamental grass.

From Danielle's purchases:

8x + 12y = 120

From Maria's purchases:

2x + 7y = 38

We can solve this system of equations using substitution, elimination, or graphical methods. Let's use the elimination method:

1. Multiply the first equation by 2 and the second equation by 8 to make the x coefficients equal:

16x + 24y = 240

16x + 56y = 304

1. Subtract the second equation from the first equation:

(16x + 24y) - (16x + 56y) = 240 - 304

-32y = -64

1. Divide both sides by -32:

y = 2

1. Substitute the value of y back into either equation to solve for x:

2x + 7(2) = 38

2x + 14 = 38

2x = 24

x = 12

Therefore, the cost of one daylily is $12 and the cost of one bunch of ornamental grass is $2.