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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

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    $\begingroup$ If $2000=.4\times x$ then what is $x$? $\endgroup$ – Jacky Chong Jan 18 '18 at 5:00
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    $\begingroup$ Welcome to MSE! I see you’re new here. If you find answers or posts good, hit the little blue arrow up (that’s called an upvote). It will move those posts higher in the feed and will reward their creators with points. If you find an answer that totally resolved your question, give it the $\color{green}{\checkmark}$ to move it to the very top and give the answerer an extra bonus. $\endgroup$ – gen-z ready to perish Jan 18 '18 at 5:24
  • $\begingroup$ @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 $x$. $\endgroup$ – symplectomorphic Jan 18 '18 at 5:47
  • $\begingroup$ @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. $\endgroup$ – gen-z ready to perish Jan 18 '18 at 5:58
  • $\begingroup$ @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. $\endgroup$ – symplectomorphic Jan 18 '18 at 8:34
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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 $60\%*\$5000=\frac{60}{100}*\$5000=\$3000$.

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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.

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If $\$2000$ is $40\%$, it is $\frac{4}{10}$ of the total. So the remaining $60\%$ would be $(\$2000/40)\cdot60=\$3000$.

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  • $\begingroup$ Use \$ to type a dollar sign in math and \% for a percentage sign. $\endgroup$ – gen-z ready to perish Jan 18 '18 at 6:01
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    $\begingroup$ @ChaseRyanTaylor thanks for he edit $\endgroup$ – QuIcKmAtHs Jan 18 '18 at 6:02
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If $\$2000$ is $40\%$, then $\$1000$ is $20\%$, hence $\$3000$ is $60\%$.

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