Final answer:
By setting up a system of linear equations to represent the purchases, we solve for the price of one daylily and one bunch of ornamental grass, finding that a daylily costs $3 and a bunch of ornamental grass costs $7.
Step-by-step explanation:
The problem presented involves determining the cost of individual items given the total cost for different quantities of those items. This is a system of linear equations problem that can be solved using substitution or elimination methods.
Let's let x represent the cost of one daylily and y represent the cost of one bunch of ornamental grass. We then have two equations based on the given information:
1. 8x + 15y = $129 (Ming's purchase)
2. 14x + 6y = $84 (Scott's purchase)
To solve this system, we can multiply the second equation by a number that will allow us to cancel out one of the variables when we add or subtract the two equations. In this case, we can multiply the second equation by 5/2 to get a new equation where the coefficient of y will be 15, the same as in the first equation.
After multiplying the second equation, we get:
3. 35x + 15y = $210
Subtracting equation 1 from equation 3 gives us:
35x + 15y - (8x + 15y) = $210 - $129
27x = $81
Hence, x = $81 / 27 = $3. So, one daylily costs $3.
Now, we substitute x = $3 into either equation to find the cost of y, the bunch of ornamental grass. Using equation 2:
14(3) + 6y = $84
42 + 6y = $84
6y = $84 - $42
6y = $42
Therefore, y = $42 / 6 = $7. So, one bunch of ornamental grass costs $7.