Answer:
[tex]x+y = 10[/tex]
Step-by-step explanation:
[tex]~~~\dfrac{53}{17}\\\\\\=3 \dfrac{2}{17}\\\\\\=3+ \dfrac{2}{17}\\\\\\=3+\dfrac{1}{\tfrac{17}2}\\\\\\=3+\dfrac{1}{8\tfrac 12 }\\\\\\=3+ \dfrac{1}{8+ \dfrac 12 }\\\\\\\text{By comparing with}~ 3 + \dfrac 1{x + \tfrac 1y},~ \text{we get}~ x = 8~ \text{and}~ y = 2.\\\\\text{Hence,}~ x +y = 8+2 =10.[/tex]
