Including a 10.5% hotel tax, your room in San Diego cost $216.58 ...

Question

Including a 10.5% hotel tax, your room in San Diego cost $216.58 per night. Find the nightly cost before the tax was added.

Accepted Answer

Welcome back. I'm so glad you're here. We are buying a one way flight ticket. Yes. Sounds brilliant. But it costs when we include the 3% fuel surcharge, $391.40. Okay, that's a little bit expensive. But maybe we're going to hawaii or something. We want to figure out the price of the ticket without that fuel surcharge. So first let's come up with our variables. Let's say that tea can be our ticket price and that's unknown. That's what we're trying to find. We know that there's a surcharge and the surcharge we're given is a percent. So the surcharge percent is 3%. We can also write that as .03 and we know that the cost with the surcharge, The total cost is going to equal $391.40. So it makes sense that if we take the ticket price and we add the surcharge that's going to equal the total cost. But note that surcharge, I put that in a different color because the surcharge is a dollar amount and were given a percentage. The surcharge is going to be the surcharge per cent Times our ticket price. So we think about it like this. The surcharge is 3% of our entire ticket cost. The surcharge Equals 3% or .03 of meaning times our ticket. And that makes sense. And now we can go ahead and use substitution. So wherever we've got our s in our equation here, we know that? S equals 0.3 t. Great. So now we've got T. Which we don't know. Plus 0.3 T. Equals our cost, which we do know is $391.40. Now we've got a couple of like terms and we can add this one T. Plus 10.3 T. And that's going to give us 1.3 T. On the left hand side and on the right it's $391.40. Now let's divide both sides by 1.3. And we get an answer of t. $380. And we want to pause and ask ourselves, does this make sense? Does it make sense that the ticket cost $380? When with the fuel surcharge? It costs $391.40. So a little bit more than that. It does make sense. Our ticket price without the surcharge should be less than the ticket with the surcharge. So we look at our answer choices in this matches with answer choice C. Well done. We'll catch on the next one

Including a 10.5% hotel tax, your room in San Diego cost $216.58 per night. Find the nightly cost before the tax was added.

Key Concepts

Percentage and Tax Calculation

Algebraic Manipulation

Solving Linear Equations

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