A ratio question that confuses most students

Alice and Olivia share some sweets in the ratio 7 : 3. Alice gives 3 sweets to Olivia and now the ratio is 5 : 3. How many sweets did each have initially?

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[MrGeorge]

I wouldn't call it a hard ratio problem but a sweet one.

[kreak]

people really hate math to call this a hard question

[shivanggupta]

This question is not even asked nowadays in clerk level exams in india 😂😂

[curryrice]

Total : Alice : Olivia = 10:7:3 = 80:56:24 ——————> Total : Alice : Olivia = 8:5:3 = 80:50:30 The difference is 6 units which is 3. 1 unit would be 0.5. Alice had 28 at first while Olivia had 12 at first

[mathexin]

I used another method.
I noticed that 7+3=10 and 5+3=8, so I multiplied the first ratio by 8:8 and the second by 10:10 so that their sums would be equal. This gave me 56:24 and 50:30, the first of which I then halved to make 28:12.

[Korohpu]

Solved this in my head by asking which multiple of 7 and which multiple of 5 had a difference of exactly 3. The lowest is 28->25. Olivias amount directly follows and lines up.

Next highest is 63->60. With a starting ratio of again 7:3, Olivia would go from 27 to 30, so you can ask the same problem with a end ratio of 2:1.

[vanshaj]

I'm dead after seeing that it is named as HARD RATIO problem

[davidsorensen]

You can also set it up as a system of equations:

a/o = 7/3
(a-3)/(o+3) = 5/3

Simplify, substitute, and solve.

[pers]

from initial ratio, the total can be a multiple of 10 say

from final ratio it can be a multiple of 8

As total sweets are same in both cases, we take LCM of 10 and 8 which is 40.

So initially A had 40*0.7 = 28, O had 12 (40-28 or 40*0.3)

After giving 3 sweets, A had 25, O has 15 ( 5:3 ratio)

[SKRamizAli]

Not even close to hard, such an easy question, and one small tip- before cross multiplying you can take common 3 from 3x+3 and cancel it with the other 3 of 5/3 🙂

[stephen]

7/10 and 3/10 originally
5/8 and 3/8 now.
8(7/10 and 3/10) and 10(5/8 and 3/8) to get common denominators. Then work out what gets Alice from 56/80 to 50/80, which we know is 3 sweets. Difference of 6 means we divide everything by 2 to get a difference of 3, so now it’s 28/40 -> 25/40, which is a difference of 3.

[MakeVarahHappen]

I worked this out and it was fun exercise for someone as a rusty at math as me.

[KoczulMoczul]

I solved it a bit differently. I set up the following system of equations:
Alice: 7x-3=5y
Olivia: 3x+3=3y
Where: x is used for the initial ratio and y for the final ratio
I didn't read the instructions carefully and got the value of y first, but for simple tasks like this, it might sometimes take longer to figure out which variable to substitute than to actually do the extra x=4/5•5=4.
For more complex tasks, however, it may be worth considering the value of which variable do you need.
Wish you guys all the best ♥️

[silverseacow]

This is a sixth grade question in my country lmao

[arghayeaye]

that wasn't a question I expected from this channel...

[terranceparsons]

Did it a lot quicker by going is it 7:3, 14:6, 21:9, 28:12?

[animezoneamv]

Well from providing MIT, Harvard, Princeton, JEE Advanced or IIT etc level questions to absolutely 6th grade school question lol. I didn't expect that truly.

[markconley]

as the total no of lollies is divisible by 10 and 8
choices are 40, 80, 120
40 fits so A had 0.7 x 40 and O had 0.3 x 40 initially

[zimzimal]

Btw it is “access maths GCSE” this is one of the easiest questions you’ll get in England

[Kasey]

Everyone says this is easy but I still don’t get it