Answer :
To find the costs of daylilies and geraniums, two equations were set up representing Jacob and Sumalee's purchases: 11D + 4G = 107 and 4D + 12G = 60. After solving this system of equations through elimination, the cost of one daylily (D) was found to be $9, and the cost of one geranium (G) was determined to be $2.
The question involves solving a system of linear equations to find the cost of daylilies and geraniums from the information provided about the purchases made by Jacob and Sumalee.
Step 1: Set up the equations based on the information given. Let D be the cost of one daylily and G be the cost of one geranium.
Jacob's purchase: 11D + 4G = 107
Sumalee's purchase: 4D + 12G = 60
Step 2: Solve the system of equations. We can use either the substitution method or the elimination method. In this solution, we'll use the elimination method.
Multiply the second equation by 2.75 (to get the same coefficient for D as in the first equation):
11D + 33G = 165
Subtract the first equation from this new equation:
(11D + 33G) - (11D + 4G) = 165 - 107
29G = 58
Divide both sides by 29 to find G:
G = 2
Step 3: Substitute the value of G into one of the original equations to find D:
11D + 4(2) = 107
11D = 107 - 8
11D = 99
D = 9
Therefore, the cost of one daylily is $9 and the cost of one geranium is $2.
Answer:
Daylily: $9
Geranium: $2
Step-by-step explanation:
1 daylily costs x.
1 geranium costs y.
11x + 4y = 107
4x + 12y = 60
Multiply the first equation by 3 and subtract the second equation from it.
29x = 261
x = 9
4x + 12y = 60
4(9) + 12y = 60
12y = 24
y = 2
Answer:
Daylily: $9
Geranium: $2
