Growing by a percentage | Linear equations | Algebra I | Khan Academy
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Growing by a percentage | Linear equations | Algebra I | Khan Academy

Let’s do some more
percentage problems. Let’s say that I start
this year in my stock portfolio with $95.00. And I say that my portfolio
grows by, let’s say, 15%. How much do I have now? OK. I think you might be able to
figure this out on your own, but of course we’ll do some
example problems, just in case it’s a little confusing. So I’m starting with $95.00,
and I’ll get rid of the dollar sign. We know we’re working
with dollars. 95 dollars, right? And I’m going to earn, or I’m
going to grow just because I was an excellent stock
investor, that 95 dollars is going to grow by 15%. So to that 95 dollars, I’m
going to add another 15% of 95. So we know we write 15% as a
decimal, as 0.15, so 95 plus 0.15 of 95, so this is
times 95– that dot is just a times sign. It’s not a decimal, it’s a
times, it’s a little higher than a decimal– So 95 plus
0.15 times 95 is what we have now, right? Because we started with 95
dollars, and then we made another 15% times what
we started with. Hopefully that make sense. Another way to say it, the 95
dollars has grown by 15%. So let’s just work this out. This is the same thing as 95
plus– what’s 0.15 times 95? Let’s see. So let me do this, hopefully
I’ll have enough space here. 95 times 0.15– I don’t
want to run out of space. Actually, let me do it up here,
I think I’m about to run out of space– 95 times 0.15. 5 times 5 is 25, 9 times 5 is
45 plus 2 is 47, 1 times 95 is 95, bring down the 5,
12, carry the 1, 15. And how many decimals
do we have? 1, 2. 15.25. Actually, is that right? I think I made a mistake here. See 5 times 5 is 25. 5 times 9 is 45, plus 2 is 47. And we bring the 0 here, it’s
95, 1 times 5, 1 times 9, then we add 5 plus 0 is 5,
7 plus 5 is 12– oh. See? I made a mistake. It’s 14.25, not 15.25. So I’ll ask you an
interesting question? How did I know that
15.25 was a mistake? Well, I did a reality check. I said, well, I know in my head
that 15% of 100 is 15, so if 15% of 100 is 15, how can
15% of 95 be more than 15? I think that might
have made sense. The bottom line is 95
is less than 100. So 15% of 95 had to be less
than 15, so I knew my answer of 15.25 was wrong. And so it turns out that I
actually made an addition error, and the answer is 14.25. So the answer is going to be 95
plus 15% of 95, which is the same thing as 95 plus 14.25,
well, that equals what? 109.25. Notice how easy I made
this for you to read, especially this 2 here. 109.25. So if I start off with $95.00
and my portfolio grows– or the amount of money I have– grows
by 15%, I’ll end up with $109.25. Let’s do another problem. Let’s say I start off with some
amount of money, and after a year, let’s says my portfolio
grows 25%, and after growing 25%, I now have $100. How much did I originally have? Notice I’m not saying that
the $100 is growing by 25%. I’m saying that I start with
some amount of money, it grows by 25%, and I end up with
$100 after it grew by 25%. To solve this one, we
might have to break out a little bit of algebra. So let x equal what
I start with. So just like the last problem,
I start with x and it grows by 25%, so x plus 25% of x is
equal to 100, and we know this 25% of x we can just rewrite as
x plus 0.25 of x is equal to 100, and now actually we have a
level– actually this might be level 3 system, level 3 linear
equation– but the bottom line, we can just add the
coefficients on the x. x is the same thing
as 1x, right? So 1x plus 0.25x, well that’s
just the same thing as 1 plus 0.25, plus x– we’re just doing
the distributive property in reverse– equals 100. And what’s 1 plus 0.25? That’s easy, it’s 1.25. So we say 1.25x
is equal to 100. Not too hard. And after you do a lot of these
problems, you’re going to intuitively say, oh, if some
number grows by 25%, and it becomes 100, that means that
1.25 times that number is equal to 100. And if this doesn’t make sense,
sit and think about it a little bit, maybe rewatch the video,
and hopefully it’ll, over time, start to make a lot
of sense to you. This type of math is
very very useful. I actually work at a hedge
fund, and I’m doing this type of math in my
head day and night. So 1.25 times x is equal
to 100, so x would equal 100 divided by 1.25. I just realized you
probably don’t know what a hedge fund is. I invest in stocks
for a living. Anyway, back to the math. So x is equal to 100
divided by 1.25. So let me make some space
here, just because I used up too much space. Let me get rid of my
little let x statement. Actually I think we know
what x is and we know how we got to there. If you forgot how we got
there, you can I guess rewatch the video. Let’s see. Let me make the pen thin
again, and go back to the orange color, OK. X equals 100 divided by 1.25,
so we say 1.25 goes into 100.00– I’m going to add a
couple of 0’s, I don’t know how many I’m going to need,
probably added too many– if I move this decimal over two to
the right, I need to move this one over two to the right. And I say how many times does
100 go into 100– how many times does 125 go into 100? None. How many times does
it go into 1000? It goes into it eight times. I happen to know that in my
head, but you could do trial and error and think about it. 8 times– if you want to think
about it, 8 times 100 is 800, and then 8 times 25 is
200, so it becomes 1000. You could work out if you like,
but I think I’m running out of time, so I’m going
to do this fast. 8 times 125 is 1000. Remember this thing isn’t here. 1000, so 1000 minus 1000 is 0,
so you can bring down the 0. 125 goes into 0 zero times,
and we just keep getting 0’s. This is just a decimal
division problem. So it turns out that if your
portfolio grew by 25% and you ended up with $100.00
you started with $80.00. And that makes sense, because
25% is roughly 1/4, right? So if I started with $80.00 and
I grow by 1/4, that means I grew by $20, because
25% of 80 is 20. So if I start with 80
and I grow by 20, that gets me to 100. Makes sense. So remember, all you have to
say is, well, some number times 1.25– because I’m growing
it by 25%– is equal to 100. Don’t worry, if you’re still
confused, I’m going to add at least one more presentation
on a couple of more examples like this.

About James Carlton

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58 thoughts on “Growing by a percentage | Linear equations | Algebra I | Khan Academy

  1. For the second problem, since 1.25 = 5/4, you can divide by 5/4 ( multiply by the inverse, 4/5) which gives you 80 without having to do long division.

  2. Mr. Hernandez had to interview a total of 63
    households in his assignment. He has already
    finished 28. What percentage of the households
    in his assignments has he finished? (Round
    your answer to the nearest tenth of a percent.)Help me

  3. @demilo1625 looks like 44.44%. just let 28/63=x/100 and cross multiply. 28/63 is the fraction you have, and some number over 100 is the fraction you want.


  5. @MrMGD92 because the questions says "it grows" which is addition. for example a crowd of 2 people grows by 5 people is the same as 2+5, so back to the problem once you find the percent you still have to add t to the whole number $95

  6. 7:10 haha "I just realised you probably dont know what a hedge fund is………I invest in stocks for living"….and probably have several yachts :p Thanks for vid!

  7. would've been better if the demo also showed that if x + 0.15x = y, then 1.15x=y, which means you can find out how much something grows by 15% multiplying by 1.15, in one step.

  8. on the excerises with the website I learned that because it comes in handy when its like 50 pounds increased by 125% so £50 (100%) + 125% = 50 * 2.25%

  9. Or instead of doing the percentage and then adding the original number, when GROWING, you can simply add +1 to your percentage, then solve and you'll get the same answer, without having to add the original number again.

  10. that is to cool you work at a hedge fund i studied finance so long and passionately but never got a spot cuz im self educated on it. buy tesla and ripple coin

  11. This is how i do the second one.
    If you have $100 after the number has grown with 25%
    $100 is 125% of the original number
    The original number is 100%.
    To find the original number you just have to divide $100 (which is the number you have after it has grown with 25%) with 125 and then you know what 1% is and times that by 100 to find the original number(100%).
    I'm bad at explaining so I'll show you my calculations:
    100/125= 0.08
    0.08*100= 80

  12. Amazing! Thank you so much for your videos. It turns out that maths is not that difficult if someone explains it properly.

  13. In the last problem,
    Portfolio grows by 25% and the current value is $100
    We need to find the initial value x

    Which means 125% of x = 100
    I.e 1.25*x=100
    X= 100/ 1.25
    X= 10000/ 125
    X= 80

  14. I think whats a bigger problem is percentages in the thousands. For example:

    From 2000, to 25,00 is 1150%. If I divide this by 28 I get approx. 41% a year.

    If I take 2000 and do a future value calculator (excel) with 41% a year, I get over 30,000,000. What am I doing wrong? How do I find what percentage growth this is per year.

    I do not get it.

  15. Literally just do .15*95 and then add the sun of that and 95 together that's the easiest way, just like he does in the video

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