Question

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Answer 1

90)

$\dfrac{5x+13y+5z+13t}{2x-5y+2z-5t} = 4 \\ \\ \dfrac{5(x+z)+13(y+t)}{2(x+z)-5(y+t)} = 4\\ \\ \text{Notam: }x+z = a,~~~y+t = b \\ \\ \dfrac{5a+13b}{2a-5b} = 4 \\ \\ 5a+13b = 4(2a-5b) \\ 5a+13b = 8a-20b~\Big|:b \\ 5\cdot \dfrac{a}{b}+13 = 8\cdot \dfrac{a}{b} - 20 \\ \\ 3\cdot \dfrac{a}{b} = 13+20 \Rightarrow 3\cdot \dfrac{a}{b} = 33 \Rightarrow \dfrac{a}{b} = \dfrac{33}{3}\Rightarrow \dfrac{a}{b} = 11 \\ \\ \Rightarrow \boxed{\dfrac{x+z}{y+t} = 11}$