Adam can rent an apartment in the city and walk to work for $615 per month. You can rent an apartment in the suburbs for $500 per month and take the train to work five dollars per day. How many days will he have to work per month to make either choice equal financially

Answer 1

Let's denote the number of days Adam works in a month as \( d \).

1. Cost of renting in the city (including walking to work):

   • Total cost = $615 per month

2. Cost of renting in the suburbs (including train fare):

   • Rent = $500 per month
   • Daily train cost = $5 per day
   • Total train cost for \( d \) days = \( 5d \)
   • Total cost = \( 500 + 5d \)

To find out how many days \( d \) make these two options equal in cost, we set the total costs equal to each other:

\[ 615 = 500 + 5d \]

Now, we can solve for \( d \):

1. Subtract 500 from both sides:

\[ 115 = 5d \]

2. Divide both sides by 5:

\[ d = \frac{115}{5} = 23 \]

Thus, Adam has to work 23 days per month for the costs of both renting options to be equal financially.