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(male narrator) In Part 1 of this video,
we began looking at revenue problems.
We set up an equation to solve this problem
regarding the college students buying a couch for $80.
We ended up with this equation, which we're now going to solve.
We can solve this rational expression
by finding the least common denominator
of n, times n, minus 5; and multiplying each term,
including the 8, by n, n minus 5.
When we do, the n's divide out, and we get 80, times n, minus 5,
plus 8n, times n, minus 5, equals--
with the n minus 5s dividing out--80n.
Continuing to solve,
we'll distribute through the parentheses,
giving us 80n, minus 400, plus 8n squared,
minus 40n, equals 80n.
Notice, we have 80n on both sides of this equation.
That's going to be convenient,
because we can quickly subtract 80n from both sides,
and those will subtract out.
Keeping everything in order, we have 8n squared,
minus 40n, minus 400 left, equals 0.
Start by factoring out the greatest common factor of 8,
leaves us with n squared, minus 5n, minus 50, equals 0.
We can continue factoring
to n minus 10, n plus 5, equals 0.
To solve, we simply have to set each factor equal to 0:
n minus 10, equals 0; and n plus 5, equals 0.
Adding 10 to both sides gives us n equals 10,
and subtracting 5 from both sides
gives us n equals -5.
If you recall from the previous video,
n represents the number of college students
who agreed to buy the couch.
We couldn't have a negative number of students,
so we have to cross the -5 out.
There must have been ten students in the original group.
The second problem we set up, we had a merchant
buying pieces of silk and selling them at a profit.
We ended up with this equation, which we can now solve
by identifying the least common denominator:
being n, times n, minus 2.
And we can multiply each term by n, n minus 2...
including the 4.
When we do this, the n's divide out,
and we're left with 70, times n, minus 2, plus 4n,
times n, minus 2, equals--
the n minus 2s divide out--88n.
Next, we can distribute through the parentheses,
which will give us 70n, minus 140, plus 4n squared,
minus 8n, equals 88n.
We can combine like terms on the n's
and put things in order
to get 4n squared, plus 62n, minus 140, equals 88n.
Subtracting 88n from both sides
will make the equation equal to 0
to give us a form we can solve:
4n squared, minus 26n, minus 140, equals 0.
We can now start factoring by pulling out the GCF of 2
to get 2n squared, minus 13n, minus 70;
and either use the quadratic formula
or continue factoring
to 2n, plus 7, times n, minus 10, equals 0.
We can now set each factor equal to 0:
2n, plus 7, equals 0; and n, minus 10, equals 0.
And solve these equations
by subtracting 7 and dividing by 2
to get n equals -7/2,
or simply adding 10 to the other equation
to get n equals 10.
You may remember this
is the number of pieces of silk the merchant bought.
He couldn't have bought a negative amount,
so he must have bought ten pieces of silk.
And this completes the problem.