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frez [133]
2 years ago
10

a positive integer is twice another. The sum of the reciprocals of the two positive integers is frac 3/16, find the two integers

Mathematics
1 answer:
gizmo_the_mogwai [7]2 years ago
4 0

Step-by-step explanation:

  • Let x be the smallest integer
  • Let 2x be the larger integer

As the sum of the reciprocals of the two positive integers is frac 3/16

So,

\frac{1}{x}\:+\:\frac{1}{2x}\:=\:\frac{3}{16}

\mathrm{Multiply\:by\:LCM=}16x

\frac{1}{x}\cdot \:16x+\frac{1}{2x}\cdot \:16x=\frac{3}{16}\cdot \:16x

Simplify

24=3x

\mathrm{Switch\:sides}

3x=24

\mathrm{Divide\:both\:sides\:by\:}3

\frac{3x}{3}=\frac{24}{3}

x=8

So,

2x=16

<h2>Verification:</h2>

\frac{1}{8}\:+\:\frac{1}{16}

\mathrm{Least\:Common\:Multiplier\:of\:}8,\:16:\quad 16

=\frac{2}{16}+\frac{1}{16}

\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}

=\frac{2+1}{16}

=\frac{3}{16}

Therefore,

\frac{1}{8}+\frac{1}{16}=\frac{3}{16}

Keywords:  word problem , integer

Learn more about solving integer word problem from brainly.com/question/10905225

#learnwithBrainly

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