Dolphin Shark fish

Mr. Dolphin and Mr. Shark were skilled fishermen. Once, they caught a total of 70 fish. Five-ninths of the fish Mr. Dolphin caught were trout. Two-seventeenths of the fish Mr. Shark caught were carp. How many fish did Mr. Dolphin catch?

Final Answer:

d =  36

Step-by-step explanation:

$$\begin{gathered} d+z=70 \\ d/9;z/17 \\ 9x+17y=70 \\ {x}_1=4 \\ {y}_1=2 \\ z=17\cdot k_2\cdot y_1 \\ {k}_2\in N \\ z=17\cdot 1\cdot y_1=17\cdot 1\cdot 2=34 \\ d=4\cdot k_1\cdot x_1 \\ d=70-z=70-34=36 \\ \text{ Verifying Solution: } \\ {p}_1=\frac{5}{9}\cdot d=\frac{5}{9}\cdot 36=\frac{5\cdot 36}{9}=\frac{180}{9}=20 \\ {k}_2=\frac{2}{17}\cdot z=\frac{2}{17}\cdot 34=\frac{2\cdot 34}{17}=\frac{68}{17}=4 \\ {p}_1\in N \\ {k}_2\in N \end{gathered}$$

The equation is a linear Diofant equation with positive coefficients

The equation has 1 positive integer solutions:

x₁ = 4   y₁ = 2  

Calculated by our Diofant problems and integer equations.

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