# 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
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 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
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.

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

1. TheDeathofGrace says:

so amazing the instinct we have when we make a mistake.

2. Jayhawkblue says:

great teacher

3. konopong says:

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.

4. brandonto says:

noob

5. demilo1625 says:

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

6. djmauropicotto says:

just divide 28/63 and it should give 0.44 which is 44%

7. iss says:

@vickiormindyb that would cause a run up of inflation.

8. iss says:

@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.

9. egyptroxs says:

GENIUS

10. uphill248 uphill248 says:

this didnt help me. can someone help me please? if i get a 2% cash back on \$19.40. how much am i getting back?

11. uphill248 uphill248 says:

@vickiormindyb THANK YOU FOR REPLAYING. BUT WHAT IS THE FORMELA FOR THIS PROBLEM? My credit card GIVE ME A 2% CASH BACK ON PURCHEASES I MAKE. I JUST WANT TO SEE IF THERE RIGHT. AND I WANT TO BE ABLE TO DO IT TOO. THANK YOU.

12. uphill248 uphill248 says:

@vickiormindyb OK THANK YOU AGAIN.

13. uphill248 uphill248 says:

@vickiormindyb Hey, thank you very much I was doing it right. I just wasn't sure. Thank you again. Bye

14. Tamizha says:

thank you

15. 9SuperMonkeyBall0 says:

No offense, but it's 14.25.

16. ktt1977 says:

Thank you!

17. nnyy10 says:

My Teacher asked Me to watch this vid >.>

18. Michael Cortez says:

@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

19. TheAnimatedAlien says:

Does something make a laughing sound at 3:40 ?

20. SEO.com says:

Great info thx

21. Byte11 says:

you heard of carrying the 1?

22. Rufus The Pink Elephant says:

Jvgvvvbb

23. TheCK1234 says:

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!

24. Jack Dick says:

25. synon9m says:

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.

26. Ghost572 says:

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%

27. MoodyJupiter9 says:

talk faster im not 4 years old

28. Mahmoud kodi says:

lol

29. Fernando J Soto says:

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.

30. Carlos Marrufo says:

13 is what percent of 47?

31. Cront Squared says:

What's a portfolio?

32. Tom Simard says:

Great job!

33. Yummy Cake says:

Woahhh, what's up with the quality?! Haha, just kidding.

34. Muneebur Rehman says:

nice.nice,very nice

35. fabian riquetti says:

100% = 95
15% is x 95×15/100=14.5 this way is easier

36. bolin wang says:

thanks, excellent explanations!

37. bolin wang says:

g

38. satisfiction says:

I always preferred doing 95×1.15

39. Dainon Earl says:

Can you post videos about investment strategies?

Very nice system

41. koss salah says:

I can't belive this video was made when I was 8

42. Jake Ambrose says:

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

43. Brandon Wiesen says:

how is 1.25x the answer to 1x + .25x ?

44. Michael says:

What is this Video quality

45. HomieTheHomie says:

This video is ollld

46. sfavdsf afbafds says:

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

47. Karolina Ambroziak says:

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

48. Jerferson de Matos says:

What is a port folio?

49. Teresa I Sanchez says:

this was very confusing

50. karifurai says:

lol 11 years ago but he still has the same mic

51. Prashanthi Dhandapani says:

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

52. Jessica T says:

You know it would be a lot easier to just use fractions..

53. Tim Yin says:

the screen is huge. lol on ur mistake

54. TheTCOLL says:

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.

55. Mathew Qian says:

7:09 thanks for answering the question

56. StUpidMonkeY_ 77 says:

Thank you Mr. Sal!!

57. kreemedits says:

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

58. Allah’s Slave says:

this was made 1 month before I was born loooooooool