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In this example we're going to be solving
percent equations.
type II equations: A% of Unknown
is B. Let's look at each example
6% of what number is 15
let's use our replacement symbols, set up our percent equation,
and see if we can solve this. So 60% as a decimal
is .60, 'of' is times
what number is X. So instead of writing a times an X, I'm just going to write
X, 0.60x is assumed to be times
'is' is equals and
my number on the right hand side is 15. I'm gonna divide
both sides by .60 I want to get
X by itself. So on the left hand side
my .60s will cancel or reduce out because they're a common
factor. 15 divided by .60
is 25 and let's do a very quick
check here, just to be sure. So if we're saying that X=25 then 60%
of 25 should equal 15, and if we multiply this on our calculator
we do indeed get 15. Second
question 25 is 12.25%
of what number. So I have 25
equals, as a decimal, 12.25% is .1225
of what number is
times X. I'm going to divide both sides by .1225
.1225
on both sides, if I do that I get X
equals 25 divided by .1225
is 204.08, that's rounded to
two decimals. If I do a check
when I multiply .1225 times
204.08
I should get approximately
25, and I get 24.9998 a
which is about 25, so we have a check.
Part 3: 175%
of what number is 325.16 so I'm going to write
175 as 1.75
'of' what number is times X equals 325.16
divide both sides by 1.75
I'm going to want to
get my X value by itself, if I perform that division on my calculator
I get one 185.81
if I do a quick check on that, I need to have 175
see 1.75 times
my result for X, and if I take that multiplication
I get approximately 325.16. I actually get
325.17 which is close enough
for our check. Last one, 20
is .14% of what number
so 20=0.0014x
and notice that sometimes we
put the 0 in front of the decimal, and sometimes we don't, just kinda varies
there's not really a rule.
So I'm going to divide both sides by 0.0014
so I get 14285.71
equals X, and if I do a little check, what I'm going to do
is I'm going to multiply .0014,
running out a room here,
time 14285.71
and I should get about 20 and in fact
I do. So again our numbers
check.