Answer:
Alia=28
Huda=12
Step-by-step explanation:
Let the constant of proportionality be x
Hence, no. of sweets Alia had initially = 7x
No. of sweets Huda had initially = 3x
No. of sweets Alia has now= 7x-3
No. of sweets Huda has now= 3x+3
We know that, the ratio of the no. of sweets Alia has now to no. of sweets Huda has now = 5:3
Hence,
[tex](7x-3) : (3x+3)=5:3\\By\ equalizing\ the\ ratios,\ we\ get,\\ 3(7x-3)=5(3x+3)\\21x-9=15x+15\\21x-15x=15+9\\6x=24\\x=4[/tex]
As we now got the constant of proportionality to be 4,
No. of sweets Alia had initially = 7*4=28
No. of sweets Huda had initially= 3*4=12
Given parameters:
Original ratio number of sweets of Alia to Huda = 7:3
Final ratio = 5:3
Alia gives 3 sweets
Huda receives 3 sweets
To solve this problem, we have to derive an algebraic equation.
Let us assume that the total number of sweets = x
So;
The ratio originally is;
7x : 3x
Alia has 7x sweets
Huda has 3x
Now Alia has (7x -3)sweets after giving out 3
Huda has (3x + 3)sweets after receiving 3
So;
7x -3 : 3x + 3 = 5 : 3
[tex]\frac{7x - 3}{3x + 3} = \frac{5}{3}[/tex]
3(7x -3) = 5(3x + 3)
21x - 9 = 15x + 15
21x -15x = 15 + 9
6x = 24
x = 4
Initially, Alia has 7x sweets = 7 x 4 = 28 sweets
Huda has 3x sweets = 3 x 4 = 12 sweets
Therefore, Alia has 28 sweets and Huda 12 sweets initially.
