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The male alpine rabbits of the Tzatzek nature reserve have suffered a disease that killed 90 of them, causing the male to female ratio to drop from 3:2 to 2:3. How many alpine rabbits lived in the reserve before the disease struck?

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22 Jan 2015, 20:46

The male alpine rabbits of the Tzatzek nature reserve have suffered a disease that killed 90 of them, causing the male to female ratio to drop from 3:2 to 2:3. How many alpine rabbits lived in the reserve before the disease struck?

Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a [#permalink]

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01 Mar 2016, 19:52

PareshGmat wrote:

Answer = B. 270

.............................. Male ......................... Female ........................ Total

Initial ........................ 3x ............................... 2x ............................ 5x (This has to be calculated)

After deaths ............... 3x-90 .......................... 2x .......................... Ratio = 2:3

Setting up the equation

\(\frac{3x-90}{2x} = \frac{2}{3}\)

4x = 9x - 270

5x = 270

So why is the first ratio the number to "x" (i.e 3x) but not the second ratio? First ratio is 3 times some number over 2 times some number, 90 of the male rabbits die, and now we have 2 over 3. Why is it not 2 times some number over 3 times some number? It seems from a logic standpoint like you treat one as a ratio representing the whole and then the second ratio specifically as a 2/3rds fraction if that makes sense.

I'm sure it's a pretty rudimentary understanding of ratios I'm just trying to figure out from the meaning stand point why you get rid of the x's on the right hand side.
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.............................. Male ......................... Female ........................ Total

Initial ........................ 3x ............................... 2x ............................ 5x (This has to be calculated)

After deaths ............... 3x-90 .......................... 2x .......................... Ratio = 2:3

Setting up the equation

\(\frac{3x-90}{2x} = \frac{2}{3}\)

4x = 9x - 270

5x = 270

So why is the first ratio the number to "x" (i.e 3x) but not the second ratio? First ratio is 3 times some number over 2 times some number, 90 of the male rabbits die, and now we have 2 over 3. Why is it not 2 times some number over 3 times some number? It seems from a logic standpoint like you treat one as a ratio representing the whole and then the second ratio specifically as a 2/3rds fraction if that makes sense.

I'm sure it's a pretty rudimentary understanding of ratios I'm just trying to figure out from the meaning stand point why you get rid of the x's on the right hand side.

You can do it that way too.

.............................. Male ......................... Female ........................ Total

I encountered a similar question and I was wondering how to solve it...

Suppose that instead of telling you specifically that the 90 dead rabbits are male, they just told you that 90 rabbits died overall.

How would you solve the problem then?

Thanks!

There would be no unique answer in that case.

Before: Male:Female = 3:2 Male = 3a, Female = 2a, Total = 5a

After: Male:Female = 2:3 Male = 2b, Female = 3b, Total = 5b

5a - 5b = 90 a - b = 18

Under this constraint, a and b can take any value. Say, a = 20, b = 2 Before: Male = 60, Female = 40, Total = 100 After: Male = 4, Female = 6, Total = 10

Say, a = 21, b = 3 Before: Male = 63, Female = 42, Total = 105 After: Male = 6, Female = 9, Total = 15

The male alpine rabbits of the Tzatzek nature reserve have suffered a disease that killed 90 of them, causing the male to female ratio to drop from 3:2 to 2:3. How many alpine rabbits lived in the reserve before the disease struck?

A. 180 B. 270 C. 360 D. 450 E. 540

Kudos for a correct solution.

Here's an algebraic solution.

Let M = the # of male rabbits BEFORE the disease struck. Let F = the # of female rabbits BEFORE the disease struck.

We're told that the male/female ratio was 3:2 BEFORE the disease. So, we can write: M/F = 3/2 Cross multiply to get: 2M = 3F -------------------------- When the disease hits, 90 male rabbits die. So, M - 90 = the # of male rabbits AFTER the disease struck. Since no females die, F = the # of female rabbits AFTER the disease struck. We're told that the male/female ratio was 2:3 AFTER the disease. So, we can write: (M - 90)/F = 2/3 Cross multiply to get: 3(M - 90) = 2F Simplify, to get: 3M - 270 = 2F -------------------------- We now have two equations: 2M = 3F 3M - 270 = 2F

Multiply the top equation by 2 to get: 4M = 6F Multiply the bottom equation by 3 to get: 9M - 810 = 6F

Since both equations are set equal to 6F, we can conclude that 4M = 9M - 810 Subtract 9M from both sides to get: -5M = -810 Solve, M = 162 To solve for F, we can use one of the equations we created earlier. Take 2M = 3F and replace M with 162 to get 2(162) = 3F Simplify: 324 = 3F Solve: F = 108

How many alpine rabbits lived in the reserve BEFORE the disease struck? So, M + F = 162 + 108 = 270 = B

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Re: The male alpine rabbits of the Tzatzek nature reserve have suffered a
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19 Jan 2018, 07:32