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## Algebra (all content)

### Course: Algebra (all content) > Unit 15

Lesson 3: Word problems with multiple units# Multiple units word problem: road trip

Sal solves a word problem where he finds the cost of gas in a road trip given the car's fuel efficiency, length of the trip, and price of gas. Created by Sal Khan.

## Want to join the conversation?

- Why is "x per y" the same thing as "x/y"?(13 votes)
- "x per y" defines a rate. Rates are just a specialized usage of fractions. The division symbol in the fraction goes where the word "per" is located. So "x per y" = "x/y"(14 votes)

- Is it just me or does it seem like Sal is making things a lot more complicated? I did the problem before Sal showed how to do it and it took a lot shorter because I just divided 400 by 25, then multiplied 16 by 3. Sorry I'm not trying to be rude or anything, but it just seems like it could be quite a bit easier(7 votes)
- I need help with this problem that I am not understanding:

If I place 1 cent on the first square of a chess board, 2 cents on the second square, and keep doubling the amount of each square, how much money will be on the 20th square?(5 votes)- You would just double the number that you have every time until you have 20 different numbers. Eg: 1, 2, 4, 8, 16, 32, 64, etc. until you have 20 numbers.(4 votes)

- Omar is going on a road trip! The car rental company offers him two types of cars. Each car has a fixed price, but he also needs to consider the cost of fuel.

The first car costs $90 to rent, and because of its fuel consumption rate, there's an additional cost of $0.50 per kilometer driven.

The graph of the cost of the second car (in dollars) as a function of the distance driven (in kilometers) is shown below.(3 votes) - A school has two types of rooms: rooms for smaller classes with 2 windows and rooms for bigger classes with 3 windows. There are 58 windows in the school, and 25 rooms. How many rooms are for smaller classes?(2 votes)
- Let 𝑆 be the number of rooms for smaller classes, and 𝐵 the number of rooms for bigger classes.

The total number of rooms is

𝑆 + 𝐵 = 25

The total number of windows is

2𝑆 + 3𝐵 = 58

From the first equation we get

𝐵 = 25 − 𝑆

Plugging this into the second equation we get

2𝑆 + 3(25 − 𝑆) = 58 ⇒ 𝑆 = 17

So, there are 17 rooms for smaller classes.(3 votes)

- wouldnt it be 25/1 and not 1/25 because of unit rate?(2 votes)
- I don't understand to know whether to use gallons per mile or miles per gallon, or dollars per mile. how do I know the unit to put as the numerator or the denominator?(2 votes)
- And really, if you just divide 400 by 25, you will get the number of gallons, and then from there multiply the gallons by the dollars and you will get your answer. Hope this helps😊(1 vote)

- How do you know when you need to multiply or divide? I realize you can do it intuitively, like if the unit you're converting to is larger (say, g -> kg), you would divide; if kg -> g, would multiply. But is there a rule to know which way to go, say if we didn't know the relative size of each unit.

Here's an example of a problem that confused me in this way if you'd like to help (particularly the 9000 min -> x days portion). Thank you.

http://imgur.com/9gEaLr6(1 vote)- Unfortunately, you must know the relative size, before you decide which operation you need to convert (multiply or divide). Then, if you like to convert the larger unit into the smaller unit, you multiply. Such as how many hours in 3 days? You must multiply 3 x 24 = 72. In the reverse, if you like to convert the smaller unit into the large unit, you must divide. Such as: How many days for 72 hours. You divide 72 by 24 (since 1 day = 24 hours).

Now, I am having a question for you: Why you posted this same question 15 times? I think this is consider inappropriate post according to the site management.(3 votes)

- What is the fuel tank size?(2 votes)
- A car can travel 25 miles per gallon on the highway and 20 miles per gallon in the city. The car's gas tank can hold 21 gallons. If the car traveled 500 miles on a full tank of gas, how many gallons were used for city driving?(2 votes)
- x in gallons on highway and y is gallons in city, so

x + y = 21

25x + 20y = 500

Try multiplying first by -20 and add to solve for x.(1 vote)

## Video transcript

Your car gets 25
miles per gallon, and you want to go on
a 400-mile road trip. Right now, gas
costs $3 per gallon. How much will the gas
for your road trip cost? So let's see. They tell us they're going
on a 400-mile road trip. 400 miles. So the first thing that I'd
want to think about is, well, how many gallons am I using? And then once I know how
many gallons I'm using, I know it's $3 per
gallon, so I can multiply the number
of gallons by $3. So to figure out the
number of gallons, would I want to
multiply 400 miles-- would I want to multiply that
times the miles per gallon, which is 25, or would I want
to multiply by the gallons per mile? Well, if I multiply by
the gallons per mile, and I multiply that
times 400, then I would get the number of gallons. So let's just think about that. I want to multiply
that times-- and I'll write the units first--
the gallons per mile. And what are the
gallons per mile? Well, we have 25
miles per gallon. We have 25 miles
for every 1 gallon. Or you could say we have 1
gallon for every 25 miles. So I really just
took the reciprocal of 25 miles per gallon and
made it 1/25 gallons per mile. Now what do we get when we
multiply these two things? The whole purpose
was to figure out how many gallons
we're going to use. Well, we see that
our miles cancel out. Miles cancel out with miles. And then I have 400
times 1/25 gallons, which is the same thing as
400 divided by 25 gallons. So this is equal to
400/25 gallons, which is the same thing as 400 divided
by 25 is equal to 16 gallons. Now it's always important
to do a reality check here, not just to try to
blindly cancel out units. Does this actually
makes sense that 16 is a much lower number than 400? Well, sure it does. And actually, if you have any
experience filling up a car, you would sense that, OK,
well, that's about the size. On around 16
gallons, a car tends to go 300 or 400 miles if it
gets pretty good fuel mileage. So that just makes
sense from experience. And it also make sense
based on how it's stated. You get 25 miles per gallon. So you're going to
need fewer gallons than you're going to need miles. So this all seems to
make sense so far. But we haven't answered
their question. They want to know, how
much will my trip cost? Right now, we've just
figured out how much fuel we're going to use. So then we could
take our 16 gallons. And to figure out
the dollar cost, are we going to multiply
it by dollars per gallon or gallons per dollar? Well, if we're thinking
just about unit conversion, we want to multiply times
the dollars per gallon. So I could write it like this. I could write it like
dollars per gallon. Actually, let me just write
out the word "dollar." Dollars per gallon. The units will cancel out. And it also makes sense. Whatever number of
dollars per gallon, I multiply it times
the number of gallons, and that's going to tell me
how much it's going to cost. This happens at the
fuel pump every day. Hey, it's $3 per gallon. I'm going to fill up 16 gallons. Hey, 3 times 16. So let's do that. So it's $3 per gallon. We see the gallons cancel out. And we are left
with 16 times $3, which is the same thing as $48. And we are done.