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

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)
I’m not sure how to solve these type of problems

I’m not sure how to solve these type of problems

Answer from: Quest

step-by-step explanation:

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