Question

Joey is planning to join a local library and is researching his options. His first option, British Library, charges a one-time enrollment fee of $\$60.00$ plus an additional monthly fee of $\$18.00$. His second option, Just Book Library, does not have an enrollment fee, but charges $\$30.00$ per month. In how many months will the total cost of a library membership at both libraries be equal?

• A. 6
• B. 3
• C. 5
• D. 15

Answer 1

The correct option is C 5

Let's start by defining our variables. Let $m$ be the number of months and $c$ be the total cost the membership.
British Library has one-time enrollment fee of $\$60.00$ plus an additional monthly fee of $\$\mathrm{18.00.}$
Therefore, equation is $c=60+18m$
Similarly for Just Book membership $c=30m$
We can solve for $m$ by setting the right hand side of both equations equal to each other
$60+18m=30m$
$60=12m$
$m=5$
The membership costs for British library and Just Book will be equal when $m=5$.