Rodney bought a 25-pound bag of dog food. His dog ate 10 2/5 pounds of the food in the first month and 10 4/5 pounds in the second month. How much dog food, in pounds, was remaining in the bag at the end of the two months?

We have been given that Rodney bought a 25-pound bag of dog food. His dog ate [tex]10\frac{2}{5}[/tex] pounds of the food in the first month and [tex]10\frac{4}{5}[/tex] pounds in the second month.

Let us find the amount of dog-food eaten by dog in two months.

[tex]\text{Dog-food eaten in 2 months}=10\frac{2}{5}+10\frac{4}{5}[/tex]

[tex]\text{Dog-food eaten in 2 months}=\frac{52}{5}+\frac{54}{5}[/tex]

[tex]\text{Dog-food eaten in 2 months}=\frac{52+54}{5}[/tex]

[tex]\text{Dog-food eaten in 2 months}=\frac{106}{5}[/tex]

Now we will subtract amount of food eaten by dog from the amount of food initially to find the remaining amount of dog food.

[tex]\text{Remaining amount of dog-food}=25-\frac{106}{5}[/tex]

[tex]\text{Remaining amount of dog-food}=\frac{5*25}{5}-\frac{106}{5}[/tex]

[tex]\text{Remaining amount of dog-food}=\frac{125}{5}-\frac{106}{5}[/tex]

[tex]\text{Remaining amount of dog food}=\frac{125-106}{5}[/tex]

[tex]\text{Remaining amount of dog food}=\frac{19}{5}[/tex]

[tex]\text{Remaining amount of dog food}=3\frac{4}{5}[/tex]

Therefore, [tex]3\frac{4}{5}[/tex] pounds of food was remaining in the bag at the end of the two months.