1286. No more data

    I was dictating a problem. I was giving the data of a system with 3 equations in 3 unknowns... A farmer had to buy pigs, ewes and hens. Datum for the 1st equation: he bought 100 animals. Datum for the 2nd equation: he spent 10 pesos per pig, 5 pesos per ewe, 1/2 peso per hen, 100 pesos in total... Then Pepe Chapuzas exclaimed: No more data, please!

    Dear Teacher:
    If the farmer bought  x  pigs,  y  ewes and  z  hens, the equations are...

x + y + z  =  100

10x + 5y + .5z  =  100

    And

x + y  =  100 − z

10x + 5y  =  100 − .5z

    And

x  =  .9z − 80

y  =  180 − 1.9z

    Then  z  must be a multiple of 10 and

80/.9  <  z  <  180/1.9

88.88  <  z  < 94.74

    So

z  =  90 hens

x  =  81 − 10  =  1 pig

y  =  180 − 171  =  9 ewes