Gorillas in a zoo! Math Problem

[IMARTIN9]

How would you solve this using the 'ratio box' study trick?



The ratio of gorillas to lions in a zoo was 5:4. After transferring 13 of the lions to another zoo, the new ratio of gorillas to lions is 7:3. How many gorillas currently reside in the zoo?


I tried setting it up like this, picking at random the total # of animals to be 45

Gorillas Lions Total
5 4 9

5 5

25 20 45



however, when I use those #s, the 7:# ratio box does not work out?

Thank you!!!!

[DavidG@VeritasPrep]

How would you solve this using the 'ratio box' study trick?



The ratio of gorillas to lions in a zoo was 5:4. After transferring 13 of the lions to another zoo, the new ratio of gorillas to lions is 7:3. How many gorillas currently reside in the zoo?


I tried setting it up like this, picking at random the total # of animals to be 45

Gorillas Lions Total
5 4 9

5 5

25 20 45



however, when I use those #s, the 7:# ratio box does not work out?

Thank you!!!!

Initially:
Gorillas: 5x
Lions: 4x

After 13 lions shipped out:
Gorillas: 5x
Lions: 4x - 13

If the ratio of Gorillas to Lions is now 7:3, then 5x/(4x-13) = 7/3
Cross-multiply: 15x = 28x - 91
-13x = -91
x = 7

Gorillas: 5x = 5*7 = 35

[DavidG@VeritasPrep]

How would you solve this using the 'ratio box' study trick?



The ratio of gorillas to lions in a zoo was 5:4. After transferring 13 of the lions to another zoo, the new ratio of gorillas to lions is 7:3. How many gorillas currently reside in the zoo?


I tried setting it up like this, picking at random the total # of animals to be 45

Gorillas Lions Total
5 4 9

5 5

25 20 45



however, when I use those #s, the 7:# ratio box does not work out?

Thank you!!!!

Note also that if you began with 25 gorillas and 20 lions and removed 13 lions, you'd have 25 gorillas and 7 lions, which is clearly not a 7:3 ratio. Moreover, the initial ratio tells us that the number of gorillas is a multiple of 5 and the new ratio tells us that the number of gorillas is a multiple of 7, so the smallest possible value for the number of gorillas is 35. If 5x = 35, x = 7. So the initial number of lions would be 4x = 4*7 = 28. If you removed 13, you'd have 15 lions. 35/15 = 7/3.

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Hi IMARTIN9,

What is the source of this question? If it's a GMAT question, then it should include 5 answer choices. In many cases, the answer choices provide a clue as to how you might go about solving the prompt. Since this question asks for the number of gorillas that currently reside in the zoo, we could use those answers 'against' the prompt and find the one that fits all of the given information. Without having those answers though, we're forced to approach this prompt algebraically (which is sometimes not the fastest way to get to the correct answer).

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

The ratio of gorillas to lions in a zoo was 5:4. After transferring 13 of the lions to another zoo, the new ratio of gorillas to lions is 7:3. How many gorillas currently reside in the zoo?
a) 35
b) 50
c) 70
d) 90
e) 105

We can PLUG IN THE ANSWERS, which represent the number of gorillas currently in the zoo.

Since G:L = 7:3, the number of gorillas must be a multiple of 7.
Eliminate B and D.

3 options remain:
A --> G=35, L=15 (since 7:3 = 35:15)
C --> G=70, L=30 (since 7:3 = 70:30)
E --> G=105, L=45 (since 7:3 = 105:45)

Before the transfer, G:L = 5:4.
Thus, the number of lions before the transfer must be a multiple of 4.
Before the transfer, there were 13 more lions:
A --> original L = 15+13 = 28.
C --> original L = 30+13 = 43.
E --> original L = 45+13 = 58.
Only A yields a multiple of 4 for the original number of lions.

The correct answer is A.

[Matt@VeritasPrep]

I'd go with

5x / (4x - 13) = 7 / 3

then cross multiply

3*5x = 7*(4x - 13)

15x = 28x - 91

91 = 13x

7 = x

Since we started with 5x gorillas, we've got 5*7, or 35.

Pretty quick and painless, and keeps the problem in one variable.