Question

George jogged a total distance of 9 1/2 miles during the months of October and November. If George only jogged 1/4 mile every day, which expression shows the number of days in which he went jogging?

Answer 1

Let's consider that he jogged for $x$ days on October and $y$ days in November. The total distance jogged is the sum of both months' distances, which implies that the following equation must hold: $$\frac{1}{4}x + \frac{1}{4}y = \text{total distance} = 9 \frac{1}{2}.$$This equation accounts for all days in which George went jogging. However, we need an expression for the number of days, and we can find it by multiplying both sides of this equation by 4. This yields $$x+y=2(9 \frac{1}{2}) = 19.$$Thus, the expression that shows the number of days in which George went jogging is $\boxed{x+y = 19}$.