Problem Solving

lheiannie07 wrote:The ratio of dogs to cats to mice at Paws and Claws Pet Shop is 3 to 5 to 4. If those are the only animals at the shop and there are 132 animals at the pet shop how many of them are mice?

A. 11
B. 33
C. 44
D. 55
E. 88

How will i set up the formulas in this problem?

OA C

We are given that the ratio of dogs : cats : mice :: 3 : 5 : 4 and the total number of dogs, cats, and mice = 132.

Number of mice at the shop = [The number of mice on ratio scale / Total number of animals on ratio scale] * Actual number of animals at the shop

= [4 / (3 + 4 + 5)] *132 = [4/12]*132 = 44.

The correct answer: C

Hope this helps!

-Jay
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lheiannie07 wrote:The ratio of dogs to cats to mice at Paws and Claws Pet Shop is 3 to 5 to 4. If those are the only animals at the shop and there are 132 animals at the pet shop how many of them are mice?

A. 11
B. 33
C. 44
D. 55
E. 88

We are given that dogs : cats : mice = 3x : 5x : 4x

Since there are 132 total animals:

3x + 5x + 4x = 132

12x = 132

x = 11

Thus, there are 4(11) = 44 mice.

Answer: C

lheiannie07 wrote:The ratio of dogs to cats to mice at Paws and Claws Pet Shop is 3 to 5 to 4. If those are the only animals at the shop and there are 132 animals at the pet shop how many of them are mice?

A. 11
B. 33
C. 44
D. 55
E. 88

One more approach:

Given: ratio of dogs to cats to mice = 3 : 5 : 4
So, some possible scenarios are:
3 dogs, 5 cats, and 4 mice
6 dogs, 10 cats, and 8 mice
9 dogs, 15 cats, and 12 mice
12 dogs, 20 cats, and 16 mice
.
.
.
IMPORTANT: Notice that the number of mice is always divisible by 4.
So, the correct answer must be divisible by 4.
ELIMINATE A, B and D

Now let's test the remaining answer choices...

Answer choice C (44 mice)
We can extrapolate our list of possible scenarios so that we have 44 mice
We get: 33 dogs, 55 cats, and 44 mice
Add the values to get: 33 + 55 + 44 = 132 PERFECT!!

Answer: C

Cheers,
Brent