So, we have an rule of three exercise:
[tex]\frac{\text{1 cup of dog food}}{10\text{ pounds}}=\frac{x}{50\text{ pounds}}[/tex]Now, we need to clear "x" in the ecuation:
[tex]\frac{1}{10}\cdot50=x[/tex][tex]x=\frac{50}{10}=5[/tex]The amount you should feed your dog each day is: 5 cups of dog food.