Решение, желательно на листике

Dear aunt marget,thank you for your letter. i was really glad when i saw it in my mailbox. i am really happy for sally that she got medical school. send my best to her.as for your and uncle john's gift for me, that's fantastic. it is just what i needed, thank you. oh, and as for my planning to go to the restaurant, it was successful! my friend had advised me that restaurant. the food was adorable. by the way, we also were given a 30%-discount card, so now we are thinking about visiting it again at the forthcoming weekend. and yes, i celebrated with my friends very well. it was a good day.now i've got to go, me and my classmates are preparing a school project.with love,egor

Пусть  х        порций     по   7руб

            у            9руб

            z           11руб

            m         13руб

            n           15руб

      Поусловию   задачи  составим    систему     уравнений.

  { x+y+z+m+n   =   180

   {7x+9y+11z+13m+15n   =    1840

   {x+y    =    z+m+n    .x+y=  180/2   =  90   >   y=90-x

   {y     =      2n   >    90-x  =  2n       n   =    (90-x)/2

   {y      =     2m  >    90-x =  2m      m  =    (90-x)/2

 

    z+m+n  =  90  Подставим   значения  m,    n    и    найдём     z

    z+(90-x)/2 + (90-x)/2  =  90  >  z+90-x  =  90 --->  z-x  =  0   >  z=x

    Полученные   значения  y,    z,    m,    n   подставим   во   второе  ур-ие

 

    7x  +9*(90-x)   +11x  +  13(90-x)/2  +15*(90-x)/2  =   1840   

    7x+810 - 9x   +11x   +  585  -13x/2    +  675   -  15x/2    =    1840

     -5x      +    2070      =         1840

     5x    =       2070    -    1840

     5x    =    230

     x       =   230/5

     x       =   46                         z   =  46

     y       =   90   -     46            y = 44

     m  =  n  =   (90   -    44)/2  =   23

 

ответ.        46,    44,     46,      23,    23.