Question

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.

Answer 1

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.

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:

$2d + 11r = 129$              Start with Jessica's equation

$\frac{2d + 11r}{2} = \frac{129}{2}$                  Divide everything in the equation by 2

$d + \frac{11r}{2} = \frac{129}{2}$                 Simplify

$d = \frac{129}{2} - \frac{11r}{2}$                 Isolate 'd' by subtracting $\frac{11r}{2}$ 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.

$5d + 7r = 97$                      Start with Arjun's equation

$5(\frac{129}{2} - \frac{11r}{2}) + 7r = 97$       Substitute 'd' for  $d = \frac{129}{2} - \frac{11r}{2}$

$\frac{5*129}{2} - \frac{5*11r}{2} + 7r = 97$      Distribute the 5

$\frac{645}{2} - \frac{55r}{2} + 7r = 97$            Simplify the numerators

$\frac{645}{2} - \frac{55r}{2} + \frac{14r}{2} = 97$          Change 7r to a fraction over 2

$\frac{645}{2} - \frac{41r}{2} = 97$                    Combine like terms, the terms with 'r'

$\frac{645-41r}{2} = 97$                       Simplify

$645-41r = 194$                 Multiply both sides by 2

$-41r = 194-645$              Subtract 645 from both sides

$-41r = -451$                     Divide both sides by –41

$r = 11$                                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.

$5d + 7r = 97$                   Start with Arjun's equation

$5d + 7(11) = 97$              Substitute 'r' for r = 11

$5d + 77 = 97$                   Simplify. Subtract 77 from both sides.

$5d = 20$                           Divide both sides by 5.

$d = 4$                              Solved for the cost of one daylily

I hope this helped! Check out a similar problem about solving systems here to learn more:

https://brainly.com/question/11103098