SOLUTION: Hi Ali and baby have some great sweets. If ali gives baba 3/8 of his sweets the ratio of ali to babas sweets is 1 to 2. What is the ratio of ali to babas sweets at first. Thanks

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Question 1204999: Hi
Ali and baby have some great sweets. If ali gives baba 3/8 of his sweets the ratio of ali to babas sweets is 1 to 2. What is the ratio of ali to babas sweets at first.
Thanks



Found 4 solutions by mananth, josgarithmetic, math_tutor2020, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Ali and baby have some great sweets. If ali gives baba 3/8 of his sweets the ratio of ali to babas sweets is 1 to 2. What is the ratio of ali to babas sweets at first.
Let ali have x sweets initially .
He gave (3/8)x to Baba
Now ratio of sweets Ali to Baba is 1:2
Let Baba have y sweets initially
x-(3/8)x /(y+(3/8)x = 1/2
(5x/8 )/((8y+3x)/8) = 1/2

5x=(8y+3x)/( 1/2)
10x = (8y+3x)
7x = 8y
x/y = 8/7

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
          initial      After

Ali         a          5a/8

Baba        b         b+3a/8

Ratio                  1/2

%285a%2F8%29%2F%28b%2B3a%2F8%29=1%2F2
5a%2F8=1%2F2%28b%2B3a%2F8%29
5a%2F4=b%2B3a%2F8
40a%2F4=8b%2B3a
10a=8b%2B3a
7a=8b
7a%2F%288b%29=1
highlight%28a%2Fb=8%2F7%29


Might be fewer steps if just multiplied both sides by 8 as the first step.

OR

Alternative Steps in the algebra
*********************************************************************

%28%285a%2F8%29%2F%28b%2B3a%2F8%29%29=1%2F2

%288%2F8%29%28%285a%2F8%29%2F%28b%2B3a%2F8%29%29=1%2F2
5a%2F%288b%2B3a%29=1%2F2
10a=8b%2B3a
7a=8b
a%2Fb=8%2F7

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Normally we go from "before" to "after", but I'll go in reverse.
Ali ends with 'a' number of candies and Baba ends with twice as much 2a.
This forms the ratio a:2a and that simplifies to 1:2 aka "1 to 2".

Then let b represent the amount Ali gifted to Baba.
Ali would start with a+b candies
Baba starts with 2a-b

After: ali = a, baba = 2a
Before: ali = a+b, baba = 2a-b

Since b is the amount Ali gives to Baba, it is equal to 3/8 of the amount Ali had before giving their sweets.

b = (3/8)(a+b)
8b = 3(a+b)
8b = 3a+3b
8b-3b = 3a
5b = 3a
b = 3a/5
b = 0.6a

Then we find the ratio of their old amounts (a+b) over (2a-b)
Plug in b = 0.6a found just now.
(a+b)/(2a-b)
= (a+0.6a)/(2a-0.6a)
= (1.6a)/(1.4a)
= (1.6)/(1.4)
= 16/14
= 8/7

In short,
(a+b)/(2a-b) = 8/7
when b = 0.6a

The fraction 8/7 leads to the ratio 8:7 aka 8 to 7
It means that for every 8 pieces of candy Ali started with, Baba has 7 pieces to start with.

Let's say hypothetically Ali started with 8 pieces of candy.
3/8 of that is 3 pieces, which is given to Baba.
Ali's amount drops to 8-3 = 5 pieces
Baba's amount increases to 7+3 = 10 pieces
Their new ratio is 5:10 which reduces to 1:2

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


You have received three responses showing very good and very different solution methods.

Now here is a fourth (using a single variable)....

Let x be the number Ali started with.

He gave 3/8 of them (i.e., (3/8)x) to Baba; the number he has left is (5/8)x.

After Ali gave Baba (3/8) of his sweets, the ratio of Ali's sweets to Baba's is 1:2, so the number Baba now has is 2*(5/8)x = (10/8)x.

So before Ali gave Baba some of his sweets, the number Baba had was (10/8)x - (3/8)x = (7/8)x.

Then the ratio of Ali's sweets to Baba's sweets in the beginning was

(x):((7/8)x) = 8x:7x = 8:7

ANSWER: 8:7