More advanced ratio problem--with Algebra (HD version)

More advance ratio problem with algebra.

[adelsalem]

This is the way i solved it in my head real quick with logic. Just check if both sides can be devided by 5 to get the ratio, if they are,
remove 15 apples and check if the ratio is 1:4 , thats it.

For every 5 apples we have 8 oranges (We dont have 15 apples to remove)
For every 10 apples we have 16 oranges (We dont have 15 apples to remove)
For every 15 apples we have 24 oranges ( if we remove 15 apples we would only have 24 oranges and the ratio would not be 1:4)
For every 20 apples we have 32 oranges( if we remove 15 apples we would have 5 apples and 32 oranges, the ratio is definitely not 1:4)
For every 25 apples we have 40 oranges ( Aha both of them can be devided by 5, we can check if the ratio becomes 1:4)

lets remove 15 apples first so
for every 10 apples we have 40 oranges ( the ratio is 1:4) Awesome, so we have a total of 50 fruits (10 apples and 40 oranges) :)

[alp]

Lets say we have x apple and y orange at the beginning.
.
we can say that x/y= 5/8   1st equation
.
after taking 15 apples we have x-15 apple. And y orange,  with the ratio 1:4
.
x-15/y= 1/4  2nd equation
.
1st equation is 8x=5y so from this equation we can say that y= 8x/5
.
2nd equation is 4x-60= y
.  
if we put the y we found in the first equation to 2nd equation
The equation will be; 
8x/5
8x
= 300
x= 25 
So at the beginning we have 25 apples and 40 oranges. (You can find the number of oranges with the ratio of 5:8.)
.
We took away 15 apples. 10 apples left and 40 oranges remains the same.
10 apples + 40 oranges = 50 fruit.

[adamthornton]

This seems like needlessly complicated solution, you just need to start with:
A/O = 5/8
A-15/O = 2/8
Cross multiply to get:
8A = 5O
8A-120 = 2O
subtract the bottom equation from the top:
120 = 3O
Solve for O:
O = 40
Substitute back and solve:
8A = 5*40
8A = 200
A = 25
And finally:
40+25-15 = 50

[jobarlives]

I too prefer the scaling method presented by spykiss72 one year ago in the comments. ie.,
"the ratio 5/8 (apples to oranges) = 5x/8x for every positive x. Remove 15 apples and the ratio becomes (5x-15)/8x = 1/4. Solve for x (x=5) to determine there were 5x=25 apples and 8x=40 oranges" jb

[Swetlana]

The new HD versions you have started are great to watch and learn!
Keep up the good work.
~Swetlana~

[manq]

you don't even need algebra to solve this question, i calculated this in my head, i multiplied 5 apples by 5 and also 8 oranges by 5 and i got 25 over 40, then i subtracted 15 apples from 25 and got 10 apples over 40 oranges then i divided both by 10 and it was 1 over 4. then 25+40=65-15 apples =50 pieces of fruits

[GenericCoder]

good here is another way to solve it.



Here is another way to solve this.
Let x = the number of we multiply apples and oranges by to get that ratio.
then we know 5x/8x = 5/8;

So 5x-15/8x = 1/4;

5x - 15 = 2x;
3x = 15;
x = 5;
So now we now how many groups are there we just multiply
5(5) - 15 + 8(5) = 10 + 40 = 50;

I hope that makes sense.

[canadadry]

We see 5a/8o - 15a =1a/4o (or 2a/8o) is the same as 5/8 - 3/8 = 2/8. 15 = 3/8 of the current ratio (not the total equation). Divide 15 by 3/8, so 15 times 8=120, divded by 3 is 40. So there are 40 oranges total, and if we divide 15 by 3 we get 1/8 of the ratio, which is 5. Multiply 5 by two (because the new ratio is 2/8) and you get 10. 10+40=50

Also, a bit of a shortcut might just be 15=3/8 so divide 15 by 3 to get 5 = 1/8. You currently have a 2/8 ratio, so 5*2=10. 5*8=40. 40+10=50.

[fatimahabib]

At that point when you published this video I was about to be born but now I am watching this because of my maths test tomorrow

[jerfersonmatos]

I've reached to this result before watching the resolution with only six lines of math on my notebook and then when I went to see the solution I didn't understand anything he said. Lucky my result was the same, so I will stick with my own way os solving this 😎

[akhilsreedhar]

For easy solution follow this :
The question can be expressed in algebraic terms as - (5x - 15)/8x = 1/4 [write this is an paper otherwise it would be hard to follow.]
Now let's cross multiply - 4 * (5x-15) = 1*8x
20x - 60 = 8x
Ie, 20x - 8x = 60
12x = 60
x = 5
Now number of apples intially = 5 * 5 = 25.
No. Of apples after 15 apples were taken = 25 - 15 = 10.
Good luck.

[thebillybobhobillybo]

@topmodel5k in case this answer isn't too late, he was saying that 5 and taking away 15 apples which is 5-15 over 8 oranges will equal the ratio of 1/4 like he said in the beginning of the problem.

[spykiss]

Your discussion on apples and oranges is too complicated. Almost all ratio problems can be more simply solved by scaling. For example, the ratio 5/8 (apples to oranges) = 5x/8x for every positive x. Remove 15 apples and the ratio becomes (5x-15)/8x = 1/4. Solve for x (x=5) to determine there were 5x=25 apples and 8x=40 oranges. Simple.

[AlexanderBollbach]

this video ramped up in complexity from the previous 26 rather steeply?

[dominikb]

ok if the first ratio is 5/8 and the second is 1/4 or 2/8 so we scale down 5 to 2 or we take away 3 that 3 is equal to 15 so 1=5 so in the end we have 10(2*5) + 40(5*8) = 50
I complicated this even more.

[weyarchive]

This is what I did :
If the original ratio was 5/8, and after 15 apples were taken away, 1/4 (2/8) were left over.
That means 3/8 completely disappeared. And the number on top, which used to be 5, is now 2. We have 3/8 left.
15 divided by 3 = 5
5 x 2/8 = 10/40
10 + 40 = 50
50 fruit remain

[chenadam]

how can i understand the context of the problem into math context???
thiss bothers me for a long time

how to tackle the problems?

[SYNKSENTURY]

the math is quite simple, but this is a very confusing video, especially in comparison to the previous videos in this playlist, which are much clearer. i followed all the steps, but i found it difficult to follow the "problem logic, " i.e., how you creatively analyze the problem in order to form the overall plan for deriving the solution. it feels like a disconnected series of operations because you aren't explaining the "story" of the relationships very well. a better way to frame this problem would be, "how many actual fruits correspond to each unit in the original ratio (5/8)?" then it's clear what we're trying to solve and what the unknowns are

[rohabatif]

Everyone has been kind enough to explain this question (which apparently nobody understood), but I can't get the solutions because we can't write fractions or send pictures in Youtube comments.

[jarjarquan]

they way I figured this out in my head took about 20 seconds and was a lot more simple