Subtracting 30 percent of which number gives 2000?

Question

Subtracting $30$ percent of which number leads to $2000$?

$$x - (30 \text{ percent of }x) = 2000$$

for example:

$$4000 - (50\text{ percent of }4000) = 2000$$

Answer 1

You want to find a number $x$ such that $x-30\%x=2000$ or equivalently $$x-\frac{30}{100}x=2000$$ which can be written as $$\frac{100}{100}x-\frac{30}{100}x=2000$$ and $$\frac{70}{100}x=2000$$ This gives $$\frac{70}{100}\times \frac{100}{70}x=2000\times \frac{100}{70}$$ which gives $$x=200\times100/7=2857\frac{1}{7}$$

Answer 2

solve $x - 0.3 x = 2000$ for x :P

Answer 3

Remember that $30\%$ of a number is equal to $0.3$ of that number. So from your equation, we have $$x - 0.30 x = 2000 \iff x(1-0.30) = 0.7x = 2000 $$ $$\iff x = \dfrac{2000}{0.7} = \dfrac{20000}{7} \approx 2857.14$$

Answer 4

Hint $$x-30\%\times x=2000\equiv x-\frac{30}{100}\times x=2000\implies x\left(1-\frac3{10}\right)=2000,x=?$$

Answer 5

What does a percent means?

It means you take a proportion of a number x. Expressed in percent, it is like if you had cut x into a hundred parts and you keep say thirty parts. That's 30%.

Cutting x into 100 parts is x divided by 100, right ? So keeping 30 parts of is $30 \times \frac{x}{100}$.

Your equation becomes : $$x - \frac{30 \times x}{100} = 2000$$

This might be something you're used to!

Answer 6

You can kind of do this without using an explicit unknown, $x$, although after a while you may well prefer using $x$.

O.K. Beginning with $100\%$, if you take away $30\%$ you end up with $70\%$ so that $2000$ is equivalent to $70\%$.

It is incorrect to write $2000=70\%$ so instead write

$$\begin{align} 70\%&\equiv 2000 \\ \Rightarrow 70\frac{1}{100}&\equiv 2000 \\ \Rightarrow \frac{70}{100}&\equiv 2000 \\ \Rightarrow \frac{7}{10}&\equiv 2000 \\ \Rightarrow \frac{1}{10}&\equiv \frac{2000}{7} \\ \Rightarrow \frac{10}{10}=100\%&\equiv 10\cdot\frac{2000}{7}=\frac{20000}{7} \end{align}$$

The notation would be

$$(P\%\equiv b)\text{ if and only if }(P\%\text{ of }x=b).$$

Answer 7

Nice answer Jimmy R.

But we can also solve it using proportion.

Since 2000 is 70 % of x.

Now, make the proportion, $$\dfrac{2000}{x}=\dfrac{70}{100}$$ $$70x=200000$$ $$x=\dfrac{200000}{70}$$ $$x=2857\dfrac{1}{7}\approx2857.14$$