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Wayne has 7/13 of the number of stamps that Monica has. After Peter gave an equal number of stamps to Wayne and Monica, Wayne has 9/10 of the number of stamps that Monica has. if the number of stamps Peter gave to Wayne is between 500 and 550, what is the number of stamps that Peter gave to Monica?

 May 14, 2022
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M has x

W has 7/13x

P give w y stamps and M y stamps.

So after that, M has x + y & w has 7/13x + y

 and 7/13x + y = (x + y) 9/10, 500 < y < 550

               7/13x + y = 9/10x + 9/10y

                     1/10y = 47/130x

                            y = 47/13x

The important is x, y lol are positive integers.

coz 500 < y < 550 => 500 < 47/13x < 550

                                   138.30 < x < 152.13

By analyzing, x should be removed by 13

13 * 10 = 130; 13 * 11 = 143; 13 * 12 = 156. Only 138 < 143 < 152

So x = 143 => y = 517

All in all P give M 517 stamps.

 May 15, 2022

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