Question

A bank offers two account plans. Their Local plan charges a $13 monthly service fee plus $3.00 for each ATM (automated teller machine)transaction beyond 6 transactions per month. Their Anywhere plan charges a $19 monthly service fee plus $1.75 per ATM transaction. For whatnumber of ATM transactions per month will the Anywhere plan cost less?Select the correct choice below and fill in the answer box to complete your choice.(Round down to the nearest whole number.)O A. For more than or equal to transactions, the Anywhere plan costs less.B. For more thantransactions, the Anywhere plan costs less.O C. For less than transactions, the Anywhere plan costs less.OD. For less than or equal to transactions, the Anywhere plan costs less.

Answer 1

Let x be the number of transactions made on ATM for each plan.

We know that their local plan charges $13 monthly and $6 for any transaction beyond six, then its cost is:

$3(x-6)+13$

Now, anywhere plan charges $19 monthly plus 1.75 for every transaction then its cost is:

$1.75x+19$

Now we want to know for how many transactions anywhere plan cost less, then we have:

$\begin{gathered} 1.75x+19<3(x-6)+13 \\ 1.75x+19<3x-18+13 \\ 19+18-13<3x-1.75x \\ 24<1.25x \\ x>\frac{24}{1.25} \\ x>19.2 \end{gathered}$

Therefore Anywhere plan will cost less for 20 or more transactions.

(we round up since we can't have a a decimal amount of transaction)