Problem Lian's dog eats $\frac{1}{20}$ of a bag of dog food each week. Lian currently has $\frac{5}{8}$ of a bag remaining. How many weeks will it take Lian's dog to finish this remaining food?

Full solution

Q. Problem Lian's dog eats

\frac{1}{20}

of a bag of dog food each week. Lian currently has

\frac{5}{8}

of a bag remaining. How many weeks will it take Lian's dog to finish this remaining food?

Identify Consumption and Remaining Amount: Identify the amount of dog food consumed each week and the remaining amount of dog food. $\newline$ Lian's dog eats $\frac{1}{20}$ of a bag each week, and there is $\frac{5}{8}$ of a bag remaining.
Calculate Weeks to Finish Food: Calculate the number of weeks it will take for the dog to finish the remaining dog food. $\newline$ To find the number of weeks, divide the remaining amount of dog food by the amount consumed each week. $\newline$ Number of weeks $= \frac{\text{Remaining amount of dog food}}{\text{Amount consumed each week}}$ $\newline$ Number of weeks $= \frac{5/8}{1/20}$
Perform Division Calculation: Perform the division by multiplying the remaining amount of dog food by the reciprocal of the amount consumed each week. $\newline$ Number of weeks = $(\frac{5}{8}) \times (\frac{20}{1})$ $\newline$ Number of weeks = $5 \times 20 / 8$
Simplify Multiplication: Simplify the multiplication to find the number of weeks. $\newline$ Number of weeks = $100 / 8$ $\newline$ Number of weeks = $12.5$
Interpret Result: Interpret the result. $\newline$ Since Lian's dog eats a whole fraction of the bag each week, it is not possible to have a half week. Therefore, we round up to the nearest whole number because the dog will finish the remaining food in the $13^{\text{th}}$ week. $\newline$ Number of weeks = $13$