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# Algebra/algebra 1

Question
(I need help to solve this word problem:) Joe spent 44 dollars on 5 rose bushes and 6 geraniums. julie spent 40 dollars on 1 rose bush and 9 geraniums. Find the cost of one rose bush and one geranium?

Hi Paola, I will be happy to help.

To answer this question, you need to form a system of equations.

Let r be the cost of 1 rose bush, and
g be the cost of 1 geranium

Joe bought 5 rose bushes. To find out how much he spent on rose bushes, multiply the number of rose bushes he bought by the cost for 1 rose bush.  This gets 5r.
Joe bought 6 geraniums, so, in a similar fashion, he spent 6g on geraniums.
Altogether, Joe spent 44 dollars, therefore adding how much he spent on rose bushes and geraniums gets the equation

44 = 5r + 6g

In a similar manner, an equation can be created for Julie
40 = 1r + 9g, or
40 = r + 9g

The system of equations for this problem is

44 = 5r + 6g
40 = r + 9g

This system can either be solved by elimination or substitution
Solving for r in the second equation gets

r = 40 - 9g

This can be substituted into the first equation to get
44 = 5(40 - 9g) + 6g

Solving,
44 = 200 - 45g + 6g
44 = 200 -39g
-156 = -39g
g = 4

So 1 geranium costs, \$4

Plug 4 in for g in the equation that is solved for r to find the cost of 1 rose bush, also \$4
This answer can be checked by plugging in 4 for r and 4 for g into the system of equations.

I hope this helps.

Anne
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment very helpful thank you:)

Algebra

Volunteer

#### Anne Losch

##### Expertise

Solving equations, graphing, evaluatin equations, factoring, functions, systems of equations, rational equations, exponent, complex numbers, word problems, logarithms, polynomials, and all topics in an Algebra 1, Algebra 2, or College Algebra class

##### Experience

I have a teaching certificate, I have taught Algebra 1 & 2 as well as tutored those subjects and tutored in College Algebra.

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NEA, past NCTM, MAA, AMS, and ASCD

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I hold a B.S. in mathematics and computer science from an accredited university and have gone back to school to get my teacher certificate. I hold more than enough credits for an education minor.

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I have worked at tutoring centers including Sylvan Learning and Huntington Learning Center. I have posted answers to mathematical questions on answers.com but would rather volunteer with AllExperts.