Hi there! Let me know if you have questions about my answer:
One shrub is $11.
One daylily is $4.
Step-by-step explanation:
To find the cost of each item, write a system of equations, one equation for what each person bought, and solve for each variable.
<u>Define your variables.</u>
let 'd' be the cost of one daylily
let 'r' be the cost of one shrub
<u>Create a system using the variables and information from the question.</u>
Write an equation for what Arjun bought:
5d + 7r = 97 5 daylilies, 7 shrubs, totaling $97
Write an equation for what Jessica bought:
2d + 11r = 129 2 daylilies, 11 shrubs, totaling $129
<u>Solve the system.</u>
I will solve the system algebraically, using the substitution method. Isolate one variable in one of the equations.
I will isolate 'd' in Jessica's equation:
Start with Jessica's equation
Divide everything in the equation by 2
Simplify
Isolate 'd' by subtracting
from both sides.
Now you have an expression for 'd'.
Substitute Arjun's equation with the expression for 'd'. Solve for 'r' to find the cost of one shrub.
Start with Arjun's equation
Substitute 'd' for
Distribute the 5
Simplify the numerators
Change 7r to a fraction over 2
Combine like terms, the terms with 'r'
Simplify
Multiply both sides by 2
Subtract 645 from both sides
Divide both sides by –41
Solved for cost of one shrub
Substitute 'r' for 11 using either Arjun's or Jessica's equation. Then, isolate 'd' to solve for the cost of one daylily.
I will use Arjun's equation.
Start with Arjun's equation
Substitute 'r' for r = 11
Simplify. Subtract 77 from both sides.
Divide both sides by 5.
Solved for the cost of one daylily
I hope this helped! Check out a similar problem about solving systems here to learn more: