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A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 5:3:1, respectively, but he wanted to make more money, so he shifted the ratio to 2:4:3, respectively. How many more acres of land were planted with tobacco under the new system?

Re: A farmer with 1,350 acres of land had planted his fields with corn, su [#permalink]

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22 Aug 2016, 07:08

Bunuel wrote:

A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 5:3:1, respectively, but he wanted to make more money, so he shifted the ratio to 2:4:3, respectively. How many more acres of land were planted with tobacco under the new system?

A. 90 B. 150 C. 270 D. 300 E. 450

Before shifting , the tobacco was \(\frac{1}{(5+3+1)} = \frac{1}{9}\) of 1,350 After shifting, tobacco became\(\frac{3}{(2+4+3)} = \frac{3}{9}\)

so the increase is\((\frac{3}{9} - \frac{1}{9}) *1,350 = 300\) acres. Answer is D

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22 Aug 2016, 07:35

Bunuel wrote:

A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 5:3:1, respectively, but he wanted to make more money, so he shifted the ratio to 2:4:3, respectively. How many more acres of land were planted with tobacco under the new system?

A. 90 B. 150 C. 270 D. 300 E. 450

Another method :

We have ratio in 5:3:1 and this is shifted to 2:4:3 ( C:S:T )

If we observe the ratio of the tobacco increased by 2 times (3-1)

T = 1/9*1350 = 150.

Since tobacco increased by 2 times..we get 150*2 = 300.

Re: A farmer with 1,350 acres of land had planted his fields with corn, su [#permalink]

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22 Oct 2017, 08:04

So just to check all the boxes we know that there are three plants, the farmer is not introducing any more plants, and that the ratios are all the same (5 + 3 + 1 = 9 and 2 + 4 + 3 = 9) so we don't have to worry about rearranging. We're only looking for the change in the acres dedicated to tobacco so the way I did it was by dividing 1350 by 9, to get 150, and then multiply it by the difference in the ratio of acreage of tobacco plants. We know that 3 - 1 = 2, so 2 is the factor we would multiply 150 by, and we'd get 300.

A farmer with 1,350 acres of land had planted his fields with corn, su [#permalink]

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22 Oct 2017, 09:41

Bunuel wrote:

A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 5:3:1, respectively, but he wanted to make more money, so he shifted the ratio to 2:4:3, respectively. How many more acres of land were planted with tobacco under the new system?

A. 90 B. 150 C. 270 D. 300 E. 450

A ratio - multiplier approach is quick, too.

Number of acres of tobacco in first scenario:

Cn: Sg: T 5x: 3x: 1x

Total of ratio parts: 5x + 3x + 1x = 9x The multiplier is x 9x = 1350 acres x = 150 acres

Tobacco = 1x = (1*150) = 150 acres

Second scenario Cn: Sg: T 2x: 4x: 3x

Sum of ratio parts still = 9x Total # of acres still = 1350 So x still = 150 Tobacco = 3x = (3*150) = 450 acres

How many more acres of tobacco in new system? 450 - 150 = 300