James and Kristin each improved their yards by planting daylilies and geraniums. They bought their supplies from the same store. james spent $120 on 8 daylilies and 12 geraniums. kristen spent $61 on 5 daylilies and 4 geraniums. Find the cost of one daylily and the cost of one geranium.
To find the cost of one daylily and the cost of one geranium, we can set up a system of equations. Let's assume that the cost of one daylily is "x" and the cost of one geranium is "y".
From the given information, we know that James spent $120 on 8 daylilies and 12 geraniums. So, the equation representing James' purchase is:
8x + 12y = 120
Similarly, Kristen spent $61 on 5 daylilies and 4 geraniums. So, the equation representing Kristen's purchase is:
5x + 4y = 61
We now have a system of equations:
8x + 12y = 120
5x + 4y = 61
We can solve this system of equations using either substitution or elimination method. Let's solve it using the elimination method.
Multiply the second equation by 3, so that the coefficients of "y" in both equations will be equal:
3(5x + 4y) = 3(61)
15x + 12y = 183
Now we can eliminate "y" by subtracting the equations:
(8x + 12y) - (15x + 12y) = 120 - 183
-7x = -63
x = (-63) / (-7)
x = 9
Therefore, the cost of one daylily is $9.
Now we can substitute this value back into either of the original equations to find the cost of one geranium. Let's use the first equation:
8(9) + 12y = 120
72 + 12y = 120
12y = 120 - 72
12y = 48
y = 48 / 12
y = 4
Therefore, the cost of one geranium is $4.
So, the cost of one daylily is $9 and the cost of one geranium is $4.
just use the facts given:
8d+12g = 120
5d+4g = 61
Now just solve the system.