Question

Jina spends $16 each time she travels the toll roads. She started the month with $240 in her toll road account. The amount, A (in dollars), that she has left in the account after t trips on the toll roads is given by the following function.=A(t)=240-16tAnswer the following questions.(a)How much money does Jina have left in the account after 11 trips on the toll roads?$(b)How many trips on the toll roads can she take until her account is empty?trips

Answer 1

GIVEN:

We are told that Jina had an opening balance of $240 in her toll road account.

Also, we are told that the amount left in the toll road account is given by the function;

`A(t)=240-16t`

Required;

(a) To find how much money she has left in her acount after 11 trips.

(b) To find out how many trips she can take until her account is empty.

Step-by-step solution;

We first take note of the variable t, which represent the number of trips taken. Also, the function shows how many trips multiplied by 16 would be subtracted from the opening balance. The result would be how much amount (variable A) would be left in her account.

Therefore;

(a) After 11 trips, Jina would have;

`\begin{gathered} A(t)=240-16t \\ \\ A(11)=240-16(11) \\ \\ A(11)=240-176 \\ A(11)=64 \\ \end{gathered}`

For the (A) part, the answer is $64.

(b) For her account to be empty, then the function given would be equal to zero. That is, after an unknown number of trips, the balance would be zero. We can now re-write the function as follows;

`\begin{gathered} A(t)=240-16t \\ \\ 0=240-16t \end{gathered}`

Add 16t to both sides of the equation;

`\begin{gathered} 16t=240-16t+16t \\ \\ 16t=240 \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }16: \\ \\ (16t)/(16)=(240)/(16) \\ \\ t=15 \end{gathered}`

This means after 15 trips she would have emptied her toll road account.

ANSWER:

`\begin{gathered} (A)=\text{\$64} \\ \\ (B)=15\text{ }trips \end{gathered}`