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Question 919327: Cha Cruz has a garden. The ratio of roses to tulips is 2 : 5, the ratio of roses to orchids is 7 : 6. Cha Cruz
wonders what the ratio of tulips to orchids is. If Cha Cruz has 183 plants, how many of each kind are there?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the ratio of roses to tulips is 2/5.
this means that you have 2 roses for every 5 tulips.
this also means you have 5 tulips for every 2 roses.
the ratio of roses to orchids is 7/6.
this means you have 7 roses for every 6 orchids.
this also means you have 6 orchids for every 7 roses.
you want to find the ratio of tulips to orchards.
since you know the ratio of roses to orchids, then find the equivalent number of tulips for every rose and you have your answer.
2 roses for every 5 tulips means that you have 5 tulips for every 2 roses which means that you have 5/2 tulips for every rose.
you can replace one rose with 5/2 tulips in your ratio of 7 roses to every 6 orchids.
the ratio of roses to orchids is equal to 7/6.
multiply 7 roses by 5/2 tulips for each rose and you get 35/2 tulips for every 6 orchids.
your ratio of 7 roses to 6 orchids becomes 35/2 tulips for every 6 orchids.
35/2 divided by 6 is equal to 35/2 * 1/6 which is equal to 35 / 12.
your ratio of tulips to orchids is therefore equal to 35/12.
you have the following ratios;
roses to tulips = 2/5
roses to orchids = 7/6
tulips to orchids = 35/12.
there are 183 plants in total.
let r = number of roses.
let t = number of tulips.
let o = number of orchids.
you get:
r + t + o = 183
since r = 2/5 * t, this means that t = 5/2 * r and you can replace t in the equation with 5/2 * r to get:
r + 5/2 * r + o = 183.
since r = 7/6 * o, this means that o = 6/7 * r and you can replace o in the equation with 6/7 * r to get:
r + 5/2 * r + 6/7 * r = 183.
you can now solve for r in the equation to get r = 42.
when r = 42, t = 5/2 * r = 5/2 * 42 = 105.
when r = 42, o = 6/7 * r = 6/7 * 42 = 36.
you will have 42 roses and 105 tulips and 36 orchids.
those are your solutions.
the ratio of tulips to orchids is 35/12.
if the total number of flowers is 183, then you have:\
42 roses
105 tulips
36 orchids
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