Arjun and Jessica each improved their yards by planting daylilies and shrubs. They bought their supplies from the same store. Arjun spent $97 on 5 daylilies and 7 shrubs. Jessica spent $129 on
2 daylilies and 11 shrubs. Find the cost of one daylily and the cost of one shrub.

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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.

Define your variables.

let 'd' be the cost of one daylily

let 'r' be the cost of one shrub

Create a system using the variables and information from the question.

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

Solve the system.

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:

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