Mathematics, 29.01.2022 01:00 cooboy

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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Answer from: missjohnson4449

Hi there! Let me know if you have questions about my

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:

Answer from: Quest

step-by-step explanation:

idk the answer i want to say 10 but then it would be equal so try 9 but then yeah so yeah we love edgen

Answer from: Quest

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation:

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