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Pierre, Kelsey and Titus shared some magnets.

Pierre took 6 more than 1/4 of the magnets.

Kelsey took 2 more than 2/3 of the rest of the magnets.

Tituts took the last 12 magnets. How many magnets did Kelsey take?

 Sep 15, 2021
 #1
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Let the number of magnets shared by the 3 boys==M
Pierre took ==1/4M + 6


M - [1/4M + 6]==3[M - 8]/4


Kelsey took ==[2/3 * 3[M - 8] / 4] + 2=[M - 4] / 2


1/4M + 6 + [M - 4] / 2 + 12 =M, solve for M


M==64 - Total number of magnets.


Pierre took ==1/4*64 + 6 ==22 magnets.
Kelsey took ==[64 - 4] / 2 ==30 magnets.
Titus took ==12 magnets
22 + 30 + 12 ==64 magnets shared by 3 boys.

 Sep 15, 2021
 #2
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Let initial no. of magnets = 12m.

 

1/4 of total : 3m

Remainder after Pierre : 12m - 3m - 6

                                        = 9m - 6

2/3 of remainder : 2/3 * (9m - 6)

                            =  6m - 4

Remainder after Kelsey : 9m - 6 - (6m - 4) - 2

                                      = 3m - 4

    Since 12 magnets remain, 3m - 4 = 12

                                               3m = 16

                                             12m = 16 + 4

                                                     = 64

  Kelsey took 6m-4+2

                     =6m-2

                    6m = 12m/2 = 32

                   6m-2 = 32-2 = 30

 Sep 15, 2021

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