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# Substituting variables and solving for an equality

Video transcript

Joey is training for a
hot dog eating contest. The person who eats the
most hot dogs in 10 minutes is the winner. If r is the number of hot dogs
that Joey can eat in a minute, and N is the total number of
hot dogs he eats in the contest, we can write the
following equation. So this makes sense. He eats a total of N hot dogs,
and the contest is 10 minutes. So you divide that by 10. So he's going to eat N
hot dogs in 10 minutes. And so, yes, this will
give you the number of how many hot dogs on
average he ate per minute. If Joey can eat 6 and
4/5 hot dogs per minute-- so they're saying
r is 6 and 4/5-- how many hot dogs does he eat
during the 10-minute contest? So they're saying, hey, what is
N going to be right over here? And so N divided
by 10 is 6 and 4/5. r, in this situation,
is 6 and 4/5. That's how many hot dogs
he can eat per minute. Now, there's a couple of ways
that you could tackle this. You could say, hey, some number
divided by 10 is 6 and 4/5. And so you say,
well, that number must be 6 and 4/5 times 10. And 6 and 4/5 times 10
would be 60 plus 8 or 68. So that's one way
you could do it, and you're essentially
multiplying both sides of this
equation by 10. The other way you could do it is
you could just try out numbers, and that usually
takes a lot longer. But at least it'll
give you the sense of how the equation relates. And especially because
they have choices here, it's not a bad idea. Obviously, the ideal one
is to just think logically through it. Hey, if something divided
by 10 is 6 and 4/5, then 10 times 6 and 4/5 is
going to be that something. And that's how you could get 68. Or if you want, you could try
out the different numbers. Look, 65 divided by 10 is
only going to give you 6.5. That's not the r
we're looking for. 56 divided by 10 is
going to give you 5.6, not the r we're looking for. 68 divided by 10 is going to
give you 6.8 or 6 and 8/10. And 6 and 8/10 is the
same thing as 6 and 4/5. So 68 works. 45 hot dogs, you
divide that by 10. You're going to get 4.5
hot dogs per minute. So all of these are completely
legitimate ways of doing it. The important thing is that you
understand this relationship and you understand how these
variables work with respect to each other.