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
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