sjuniv32
A farmer has two plots of land of different sizes, and each plot of land consists of two different crops, corn, and wheat. In one plot, the ratio of corn to wheat by land area is 7 to 3, and in the other plot, the ratio of corn to wheat by land area is 11 to 4. If the ratio of corn to wheat by land area of the two plots combined is 24 to 9, what is the ratio of the total area of the smaller plot to the total area of the larger plot?
A) 2 to 5
B) 3 to 8
C) 1 to 4
D) 2 to 9
E) 3 to 16
Set the ratio of the second land to the first land as x. Then to get 24/9 in the terms of the first land and second land, we need total corn over total wheat. We can treat the first land's area as 1 and the second land's area as x since the result is a ratio:
\(\frac{\frac{7}{10} + \frac{11}{15}*x}{\frac{3}{10} + \frac{4}{15}*x} = \frac{24}{9} = \frac{8}{3}\)
\(\frac{7}{10} + \frac{11}{15}*x = \frac{4}{5} + \frac{32}{45}x\)
\(\frac{1}{45}x = \frac{4}{5} - \frac{7}{10} = \frac{1}{10}\)
\(x = 9/2\).
Now we know the second land is bigger but we want the ratio of the smaller land to the bigger land, so we reverse it to get 2:9.
Ans: D