huong and kathyrn each day impeoved their yards by planting rose bushes and ornamental grass. they bought their supplies from the same store. huong spent $70on 14 rose bushes and 7 bunches of ornamental grass. kathyrn spent $71 on 5 rose bushes and 14 bunches of ornamebtal grasa. what is the cost of one rose bush and the cost od ine bunch of ornamental geass?

We can set up a system of equations to solve for this. Let cost of 1 rose bush be r and cost of 1 ornamental grass be g. Thus we can form 2 equations:

[tex]14r+7g=70\\5r+14g=71[/tex]

We can multiply the first equation by -2 so that we can eliminate g. Thus, we have:

[tex](*-2)14r+7g=70\\5r+14g=71\\-------\\-28r-14g=-140\\5r+14g=71\\--------\\-23r=-69\\r=\frac{-69}{-23}=3[/tex]

Thus, 1 rose bush is $3. Now plugging in r = 3 into the first original equation, we can solve for g:

[tex]14r+7g=70\\14(3)+7g=70\\42+7g=70\\7g=70-42\\7g=28\\g=\frac{28}{7}=4[/tex]

Thus, 1 bunch of ornamental grass is $4.