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1/3 of the animals are dogs

by Mike
(PA)











































1/3 of the animals are dogs, 2/12 of the animals are cats, their are 19 other animals, how many are in the shelter

Comments for 1/3 of the animals are dogs

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Apr 08, 2011
Word Problem - Proportions
by: Staff


The question:

by Mike
(PA)

1/3 of the animals are dogs, 2/12 of the animals are cats, their are 19 other animals, how many are in the shelter


The answer:

1/3 of the animals are dogs, 2/12 of the animals are cats, their are 19 other animals, how many are in the shelter

To solve this problem, solve two equations with two unknowns


1st equation

Fraction of animals which are dogs (= 1/3) + Fraction of animals which are cats (= 2/12) + Fraction of animals which are other animals (unknown value) = 1 (a total fraction of 1/1 = 100% of all animals)


2nd equation

Total animals in shelter (unknown value) * Fraction of animals which are other animals (unknown value) = 19


Solving the 1st equation


Fraction of animals in the shelter which are dogs: 1/3

Fraction of animals in the shelter which are cats: 2/12

Fraction of animals in the shelter which are other animals: F (unknown)

The total of all three fractions must = 1 (a total fraction of 1/1 = 100% of all animals)

Fraction of animals which are dogs + Fraction of animals which are cats + Fraction of animals which are other animals = 1


1/3 + 2/12 + F = 1

1/3 + (1 * 2)/(6 * 2) + F = 1

1/3 + (1/6) * (2/2) + F = 1

1/3 + (1/6) * 1 + F = 1

1/3 + 1/6 + F = 1


To convert the first fraction to a common denominator with the second fraction, multiply the first fraction by another fraction: 2/2

Note that 2/2 = 1, so the first fraction is only being multiplied by 1. Its value has not changed.


(1/3)*(2/2) + 1/6 + F = 1

Multiply the numerators of the two fractions together, and multiply the denominators of the two fractions together.

(1*2)/(3*2) + 1/6 + F = 1

2/6 + 1/6 + F = 1


Add the two fractions: 2/6 + 1/6

(2+1)/6 + F = 1

3/6 + F = 1


Reduce 3/6 to its lowest terms

(1*3)/(2*3) + F = 1

(1/2)*(3/3) + F = 1

(1/2)*(1) + F = 1

(1/2)*1 + F = 1

1/2 + F = 1


Subtract ½ from each side of the equation

1/2 - 1/2 + F = 1 - 1/2

0 + F = 1 - 1/2

F = 1 - 1/2

F = 1/2

Fraction of animals in the shelter which are other animals = 1/2



Solving the 2nd equation


Total animals in shelter * Fraction of other animals = total number of other animals

Total animals in shelter * 1/2 = 19


Divide each side of the equation by ½

(Total animals in shelter * ½)/(1/2) = 19/(1/2)


Reverse the ½ to the fraction 2/1, and then multiply.

(Total animals in shelter * ½)*(2/1) = 19/(1/2)

(Total animals in shelter)*(1/2)*(2/1) = 19/(1/2)

(Total animals in shelter)*(1*2/2*1) = 19/(1/2)

(Total animals in shelter)*(2/2) = 19/(1/2)

(Total animals in shelter)*(1) = 19/(1/2)

(Total animals in shelter)*1 = 19/(1/2)

Total animals in shelter = 19/(1/2)

Total animals in shelter = 19 * (2/1)

Total animals in shelter = (19 * 2)/1

Total animals in shelter = 38/1

Total animals in shelter = 38


The final answer is: 38 animals are in the shelter



Thanks for writing.


Staff
www.solving-math-problems.com



Mar 04, 2013
1/3 dogs
by: Anonymous

It's impossible! How many dogs and how many cats? 19 other animals is 1/2. So 19 =1/2. 2/12..or 1/6 are cats which leaves 1/3 or 2/6 are dogs. Now try to figure out what 1/6 of 19 is......So you have 6.333333 cats and 12.6666666 dogs........imposible with the word problem the way it is stated.

Mar 06, 2013
1/3 dogs
by: Staff

The original question does not ask how many dogs or cats are in the shelter.

The question ONLY asks for the total number of animals in the shelter.

The total number of animals in the shelter is 38.

Everything is OK if you stop there.

Once you try to calculate the number of cats and dogs, the problem falls apart.

As you have correctly pointed out, 1/6 of 38 is indeed 6.333333 cats. 1/3 of 38 is 12.6666666 dogs.

Whoever originally wrote the problem didn't think it through.


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