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A farmer has an apple orchard consisting of Fuji and Gala apple trees.
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03 Apr 2021, 00:50
03 Apr 2021, 00:50
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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?
A. 22
B. 33
C. 55
D. 77
E. 88
A. 22
B. 33
C. 55
D. 77
E. 88
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Re: A farmer has an apple orchard consisting of Fuji and Gala apple trees.
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03 Apr 2021, 20:51
03 Apr 2021, 20:51
1
GeminiHeat wrote:
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?
A. 22
B. 33
C. 55
D. 77
E. 88
A. 22
B. 33
C. 55
D. 77
E. 88
Let Fuji trees be \(F\)
Gala trees be \(G\)
Pure Fuji be \(PF\)
Pure Gala be \(PG\)
Cross-Pollinated be \(C\)
Now, \(C = \frac{10}{100}(F + G)\)
\(PF = \frac{3}{4}(F + G)\), and
\(PF + C = 187\)
\(\frac{3}{4}(F + G) + \frac{10}{100}(F + G) = 187\)
\(0.85 F + 0.85G = 187\)
\(F + G = \frac{187}{0.85} = 220\)
Therefore, \(PG = 220 - 187 = 33\)
Hence, option B
Re: A farmer has an apple orchard consisting of Fuji and Gala apple trees.
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04 Apr 2021, 03:06
04 Apr 2021, 03:06
1
Let the total trees be x
3/4 are pure Fuji = 3x/4
10% cross pollinated = x/10
now The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187
3x/4 + x/10 = 187
solve this x = 220
220-187 = 33 are the pure Gala trees.
3/4 are pure Fuji = 3x/4
10% cross pollinated = x/10
now The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187
3x/4 + x/10 = 187
solve this x = 220
220-187 = 33 are the pure Gala trees.
