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by dmateer25 » Wed Dec 24, 2008 5:51 am
A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?


22
33
55
77
88


B
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Re: PS 1

by parallel_chase » Wed Dec 24, 2008 6:14 am
let total no. of trees be x

10%x = cross pollination

combined fuji = 187

pure fuji = 3x/4

only fuji = combined fuji - cross pollination

3x/4 = 187 - x/10

x = 220

pure fuji = 220*3/4 = 165

total = pure F + pure G + 22[both cross pollination]

220 = 165 + G +22

220 - 187 = G

33 = G

Hope this helps.
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by Mozartain » Wed Dec 24, 2008 8:12 am
Pure fuji = 3/4 of total
cross-pollinated = 1/10 of total

together they are 3/4+1/10=15/20+2/20=17/20

so pure gala = 3/20 of total

set up the ratio:
187/17=?/3
?=33

(the ratio above says: if 17 parts mean 187 then 3 parts mean how many? while setting up such ratios, all you have to do is put corresponding items in similar places. eg. we could also write 3/17 = ?/187. here the ratio says: what number has the same multiplicative relationship with 187 as 3 has with 17)
Last edited by Mozartain on Wed Dec 24, 2008 9:27 am, edited 1 time in total.
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by amitabhprasad » Wed Dec 24, 2008 9:14 am
@ parallel_chase
I am little confused by the wording
doesn't
while 3/4 of all his trees are pure Fuji
means 3/4th of 90% of x ??? as 10% seeds were pollinated ?
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by parallel_chase » Wed Dec 24, 2008 9:24 am
amitabhprasad wrote:@ parallel_chase
I am little confused by the wording
doesn't
while 3/4 of all his trees are pure Fuji
means 3/4th of 90% of x ??? as 10% seeds were pollinated ?
10%x = pollinated

90%x = pure G + pure F

we know that x=220

198 = G + 165 [pure F = total F - 10% polinated] or [3/4*220]

x = 198-165 = 33


Hope its clear.
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by vittalgmat » Sat Dec 27, 2008 1:04 am
Here is another way:

Let F = pure Fuji,
G = pure Gala
FG = crosspollinated.

T = F + G +FG ---------------(0)

We are given
F + FG = 187. -----------------(1)
F = 3/4 of total ==> 3T/4 -----------(2)

FG = 1/10 of Total -----------------(3)

So 3T/4 + T/4 = 187
Solving, T = 220.

Now back substituting T = 220 in (0)

220 = G + 187
So G = 33

HT Helps.
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