SOLUTION: jack spent $22 on 4 rose bushes and 2 pots of ivy. Kim spent $22 on 1 rose bush and 6 pots of ivy. Whats the cost for one rose bush and one pot of ivy?

Question 1027246: jack spent $22 on 4 rose bushes and 2 pots of ivy. Kim spent $22 on 1 rose bush and 6 pots of ivy. Whats the cost for one rose bush and one pot of ivy?
Answer by purpleoj(8) (Show Source): You can put this solution on YOUR website!
First, write what you know as an equation.
Jack spent $22 on 4 rose bushes and 2 pots of ivy.
Therefore,

(Note: "r" means rose bushes and "p" means pots of ivy.)
Kim spent 22 dollars on 1 rose bush and 6 pots of ivy.

Now, note that the price is the same. This means that we can logically say that , and, by simplifying, .
Now, if we find one value, we can use the above equation to find the other.
Now, (bear with me here) we multiply both sides of the top equation by -3 and get

Now, I'm going to do elimination by adding the top and bottom equations together. (I have neither room nor time to explain elimination, but if you look it up, I'm sure you'll get an answer.)

which, simplified, is
.
Divide -44 by -11 and you get

So we know that rose bushes cost 4 dollars, but now, we can use our handy-dandy equation () by plugging in 4 for r.

Wait! Normally you would multiply the 3 and 4 together and get -12, but since both sides share a 4, we can divide both sides by 4 and get
.
Voila!
A rose bush is four dollars and a pot of ivy is three dollars.
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