How do you solve this?

By using the subsitution/elimination method...





A florist will make up bouquets of different flowers. The rates and bouquets are listed below. If the flowers cost the same individually or in a bouquet, how much does one orchid cost?





Small bouquet:


2 snapdragons, 1 rose, 1 orchid $8


Medium bouquet:


5 snapdragons, 3 roses, 2 orchids $19


Large bouquet:


8 snapdragons, 5 roses, 5 orchids $38





Ah, I'd really appreciate the clarification! It's a study question of mine and I'm a bit confused..

How do you solve this?
Ok this took me about a minute but what you do is you find different prices that could add up to 8(for the first one) and well after i found out that 1 dollar orchids didn't work then i did 2 dollar orchids... nope then i did 3... nope then at-last i did 4 dollar orchids 2 dollar roses and 1 dollar snapdragons.
Reply:I've never done three variable simultaneous equations, but these sites might help you:





http://www.mathreference.com/la-det,sime...


http://www.allaboutcircuits.com/vol_5/ch... (scroll down)


http://www.themathpage.com/alg/simultane...
Reply:umm possibly the worst way to go about solving these types of questions is through guess and check it works .0000000001% of the time and i almost guarantee you will never finish a math test if you guess. So to go about solving this type of problem you just solve it like a regular two variable simo equation





first you need to make three equations since you have three unknowns.





let x = snapdragons y = roses and z = orchids





EQUATIONS:





2x + y + z = 8


5x + 3y + 2z = 19


8x + 5y + 5Z = 38





Now that we have three equations just pick one of them in this case i pick 8x + 5y + 5z = 38. Since we are looking to find out z first we can take out x and y first ill start off with x.





40x + 20y + 20z = 160


40x + 24y + 16z = 152


-40x - 25y - 25z = -190





After we find a common multiple of x which is 40 we can now use linear combination on the two equations above -40x - 25y - 25z = -190. You should get





-5y - 5z = -30


-y - 9z = -38





Now we take out y so





-5y - 5z = -30


5y +45z = 190





combine and you get


40z = 160


4z = 16


z = 4





So Orchids cost 4 dollars to find out what dragons and roses cost just plug in z to find out y and x. So for example to find out y just plug z into the equations -y - 9z = -38. Then after you find y just plug z and y into one of the three variable equations.





Although there is another way easier way to solve it which is to use matrices. Its pretty much impossible to show you this other method using yahoo answers.