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Tom has a certain number of marbles. He gave Bob 1/4of them. Bob gave 1/3 of his share to John. John then gave 1/2 of those to Kevin. Kevin is left with 5 marbles after giving 1/6 to Michael. How many marbles did Tom have? A. 72 B. 60 C. 136 D. 144​

Sagot :

Using proportions, it is found that the number of marbles that Tom had is given by:

  • D. 144​

Proportions

  • Initially, Tom had x marbles.
  • He gave Bob [tex]\frac{1}{4}[/tex] of it, that is, [tex]\frac{1}{4}x[/tex].
  • Bob gave [tex]\frac{1}{3}[/tex] of his share of [tex]\frac{1}{4}x[/tex] to John, hence John's amount is [tex]\frac{1}{12}x[/tex].
  • Kevin receives half of John, hence Kevin's amount is [tex]\frac{1}{24}x[/tex].
  • After giving [tex]\frac{1}{6}[/tex] of his amount to Michael, Kevin is left with 5 marbles, that is, [tex]\frac{5}{6}[/tex] of his amount of [tex]\frac{1}{24}x[/tex] is 5.

Then:

[tex]\frac{5}{6}\left(\frac{1}{24}x\right) = 5[/tex]

[tex]\frac{5}{144}x = 5[/tex]

[tex]x = 144[/tex]

Hence, option D is correct.

To learn more about proportions, you can take a look at https://brainly.com/question/24372153

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