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     x +  y = 25      (1)    (counting coins)
    5x + 1y = 53      (2)    (counting money)
Subtract equation (1) from equation (2) and solve for x
     4x     = 53 - 25 = 28
      x               = 28/4 = 7.
ANSWER.  7 5-peso coins and the rest, 25-7 = 18 1-peso coins.
CHECK.   7*5 + 18*1 = 35 + 18 = 53 Php.    ! Precisely correct !
Solved.