Question

Assem is staying in a resort. The charges of the resort is \[\$ 99.95\] per night plus tax for a room. A tax of \[8\% \] is imposed on a room rate. An additional one-time untaxed fee of \[\$ 5.00\] is charged by the resort. Find the total cost if Aseem is staying for x nights

Answer 1

Hint: We will find the charge of room for x nights using the amount given for one night because the basic rent for the room is being asked for x nights, and then we will multiply it with the given tax percentage since it is given that some percentage of the task is imposed on the room rate, and finally we will add everything with the fixed cost, to get the total charge as we are requested to find the total charge of the room for x days.

Formula used:
Total cost= Fixed cost + Variable cost
Fixed costs (FC) are costs that don't change from month to month and don't vary based on activities or the number of goods used. The formula to calculate total cost is the following: TC (total cost) = TFC (total fixed cost) + TVC (total variable cost)

Complete step by step answer:
The total charge that Assem will pay is the room rate and the \[8\% \] tax on the room rate and a fixed fee of \[\;\$ 5.00\]
It is given that, Charges of resort per night is \[99.95\]
If Assem stayed \[x\]nights,
Then the charge for \[x\] nights is \[99.95 \times x\]
\[99.95 \times x = \]\[99.95x\]
It is given that a tax of \[8\% \] that is \[0.08\] times the rent is imposed on a room rate.
Here we know that \[8\% = \dfrac{8}{{100}} = 0.08\] by using the percentage formula.
A tax of a room rate for one night is \[0.08 \times 99.95\]
Therefore, the tax of a room rate for\[x\]nights is \[0.08 \times 99.95 \times x = 0.08 \times 99.95x\]
Also it is given that there is a onetime fixed fee of \[\;\$ 5.00\]
Thus sum of all the amount will lead us to the required rent of the room,
That is the total charge of the room for \[x\] nights is \[ = \left( {99.95x + 0.08 \times 99.95x} \right) + 5\]
\[ = 1.08\left( {99.95x} \right) + 5\]
Simplifying the above term we get the amount Assem has to pay for a \[x\] night stay.

The total charge Assem has to pay is \[ = 107.946x + 5\]

Additional information:
Total cost (TC) is the total economic cost of production and is made up of variable cost, which varies according to the quantity of a good produced and includes inputs such as labor and raw materials, plus fixed cost, which is independent of the quantity of a good produced and includes inputs that cannot be varied in the short term.

Note:
While finding the percentage of tax imposed on a room for one day we multiply the percentage value with the rent for the room for a day. To find the percentage of tax for $x$ nights we should add the tax for a day ‘$x$’ times that is we have multiplied the tax imposed by $x$.