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vfiekz [6]
2 years ago
12

Arjun and Jessica each improved their yards by planting daylilies and shrubs. They bought their

Mathematics
1 answer:
Anvisha [2.4K]2 years ago
7 0

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:

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:

brainly.com/question/11103098

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