# if $2000 is 40% what is the remaining 60% I am sure it is a simple equation, but I just can't seem to figure this one out. if$2000 is 40% how do i figure out what the remaining 60% is in dollars

• If $2000=.4\times x$ then what is $x$? – Jacky Chong Jan 18 '18 at 5:00
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• @JackyChong: to be fair, that's not what the question asks. It asks "If $2000=0.4x$, then what is $\color{red}{0.6}x$?" No need to detour through $x$. – symplectomorphic Jan 18 '18 at 5:47
• @symplectomorphic I believe that’s why Mx. Chong posted a comment and not an answer. We also call those hints, because they nudge learners along he right path. – gen-z ready to perish Jan 18 '18 at 5:58
• @ChaseRyanTaylor: the substance of my comment is that the nudge Jacky made is to the wrong path. To transform $0.4x$ into $0.6x$ one need not solve for $x$; one simply has to multiply by $1.5$. Your presumption that I missed the fact that Jacky's comment is a hint is totally groundless. Of course it's a hint. It's just not a very good one. – symplectomorphic Jan 18 '18 at 8:34

## Method using ratios

Let the answer be $x$.

$$\frac{\2000}{40\%}=\frac x{60\%}$$

$$x=\frac{\2000\cdot60\%}{40\%}$$

$$x=\frac{\2000\cdot3}{2}$$

$$x=\3000$$

## Method using the total sum

Because $\$2000$is$40\%$of total, then$\$1000$ is $20\%=\frac15$ of total, so the total is $5*\$1000=\$5000$.

So, $60\%$ of total is $60\%*\$5000=\frac{60}{100}*\$5000=\$3000$. Percentages are very cool. As you know,$\%$just stands in for$\times\frac{1}{100}$, but what you may not know is that to take a percentage of something, you just have to multiply by that percentage: $$\text{x\% of N}=(x\%)(N)=\frac{xN}{100}$$ So, call the total money$T$. Saying that$\$2000$ is $40\%$ of $T$ tells us that

$$\2000 = 0.4T \iff T=\frac{\2000}{0.4}$$

Now, to get the remaining $60\%$, take

$$(60\%)T = (0.6)\frac{\2000}{0.4}$$

I’ll let you do the arithmetic.

If $\$2000$is$40\%$, it is$\frac{4}{10}$of the total. So the remaining$60\%$would be$(\$2000/40)\cdot60=\$3000$. • Use \$ to type a dollar sign in math and \% for a percentage sign. – gen-z ready to perish Jan 18 '18 at 6:01
• @ChaseRyanTaylor thanks for he edit – QuIcKmAtHs Jan 18 '18 at 6:02

If $\$2000$is$40\%$, then$\$1000$ is $20\%$, hence $\$3000$is$60\%\$.