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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

how did you get the second one, \(\frac{7}{10} + \frac{11}{15}*x = \frac{4}{5} + \frac{32}{45}x\)
this eqn ?
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Hi sthahvi ,

I had \(\frac{\frac{7}{10} + \frac{11}{15}*x}{\frac{3}{10} + \frac{4}{15}*x} = \frac{8}{3}\) and if I move \(\frac{3}{10} + \frac{4}{15}*x\) to the right side I will obtain the second equation.

\(\frac{4}{5}\) comes from \(\frac{8}{3}\) times \(\frac{3}{10} \) and \(\frac{32}{45}\) comes from \(\frac{8}{3}\) times \(\frac{4}{15}\). Hope this helps!

("@" me next time for a faster reply!)
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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



For such problems, I find alligations the quickest way.

I took the corn portion i.e 7/10, 11/15 and 24/33. I first got all denominators equal and that makes my fractions as 231/330, 242/330 and 240/330. By finding the distance between 240/330 and 231/330 I get 2 and the distance between 242/330 and 240/330 I get 9. Hence the ratio is 2:9.

Hope this is useful.
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The problem seems extremely hard. Is it possible to solve in two minutes?
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Russ19
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

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