Word problem

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Word problem

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

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Apr 08, 2011
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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

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