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(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

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.



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Anne Losch


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