When number is decreased by 10% of itself, result is 108.

[oldbones.evelyn]

When a number is decreased by 10% of itself, the result is 108. What is the number?
The number is?
The problem is: x-0.1x = 108
Then it comes up: x-0.9 = 108
I don't understand where the 0.9 comes from?

Help! Thank you Evelyn

 

[masters]

Re: decreasing % of itself.

When a number is decreased by 10% of itself, the result is 108. What is the number?
The number is?
The problem is: x-0.1x = 108
Then it comes up: x-0.9 = 108
I don't understand where the 0.9 comes from?

Help! Thank you Evelyn

Hello Evelyn,

\(\displaystyle x\) is considered to be \(\displaystyle 1x\) or 100% x or \(\displaystyle 1.00x\), so when you subtract \(\displaystyle x-0.1x\), that's the same thing as saying \(\displaystyle 1.00x - 0.1x = .9x\)

That's how we get \(\displaystyle x-0.1x=108\Longrightarrow.9x=108\Longrightarrow\boxed{x=120}\)

 

[stapel]

The problem is: x-0.1x = 108

This is the equation that you need to solve in order to find the (numerical) answer the (worded) number "problem". :wink:

Then it comes up: x-0.9 = 108

I don't know what "it" might be, or from whence "it" might be "coming up", but "it" is incorrect, since 0.1x equals 0.9 only for x = 9. :shock:

Instead, try doing the algebra yourself:

. . . . .the whole value: x
. . . . .ten percent, as a decimal: 0.1
. . . . .ten percent of the whole value: 0.1x
. . . . .the whole value, decreased by ten percent: x - 0.1x

Then note:

. . . . .x - 0.1x = 1.0x - 0.1x = (1.0 - 0.1)x = ...?

What do you get?

Eliz.

 

[sgtpepper]

Another way you could see where 0.9 comes from (which is very similar to and basically the same thing masters said)

the original equation:

(x - 0.1x)= 108

then factor out the x:

x(1 - 0.1) = 108 ----------- right?

then:

(1 - 0.1) = 0.9

so:

x(1 - 0.1) = 108 =
x(0.9) = 108

your (x - 0.9) = 108 is probably someone's typographical/mathematical error, as it should read x0.9 or 0.9x

Solving for x:

x = 108/(0.9)
x = 120

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