WEBVTT
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Hello.
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Welcome to Week 4.
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Let us consider
the introduction,
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types of equations step.
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And let us start with
the first exercise.
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It's a problem about cherries.
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Precisely, the question is, how
many cherries were on the table
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if, after we ate
4/5 of those, we
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remain with three times the
initial amount minus 42?
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This problem can be easily
solved with an equation.
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Let us see.
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Call x the initial number
of cherries on the table.
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Then the exercise gives
us some information.
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What do we know?
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That after we ate
4/5 of those, we
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remain with three times the
initial amount minus 42.
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Ok then, this is
the initial amount.
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After we have eaten
the 4/5 of those,
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we remain with the initial
amount minus the 4/5
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of the initial amount.
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And we know, from the
text of the exercise,
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that this is equal to three
times the initial amount
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minus 42.
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This is just a translation of
the problem in an equation.
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And what do you get?
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This is a linear equation.
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Very easy to solve,
but let us see.
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We get x minus 4/5 x minus
3 times x equal to minus 42.
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And then let us collect
together the coefficients of x.
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And we have 5 over
5 which is 1 minus 4
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over 5 minus 3 times 5 over
5, x equal to minus 42.
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And this is exactly, we have
5 as common denominator.
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And you have 5 minus 4,
which is 1, minus 15.
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1 minus 15 is minus 14.
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Then we have that this fraction
has to be equal to minus --
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times x has to be
equal to minus 42.
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Then, now we can multiply
on both sides by minus 1.
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And we get 14 over
5x equal to 42.
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We can divide on
both sides by 14.
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Indeed, divide by 14 is
exactly like to divide by 7,
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and then divide by 2.
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If we divide by 7 42, we get 6.
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And then we divide
by 2, we get 3.
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Therefore, we remain
with the equation
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x equal, you multiply it by 5
on both sides, x equal to 15.
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Therefore, the initial
amount of cherries was 15.
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Thank you.
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