Initially, Alice had 28 sweets and Olivia 12 sweets.
Step-by-step explanation:
First assume that Aunty Joan has x number sweets.
Alice and Olivia shared the x sweets in a ration of 7:3, this means
Alice had 7/10 x sweets and Olivia had 3/10 sweets.
Alice gives 3 sweets to Olivia, Alice will remain with ;
![\frac{7}{10} x-3](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B10%7D%20x-3)
Then the new ratio changes to 5:3 which means Alice will have 5/8 x number of sweets.
Equate the number of sweets for Alice in the two cases, which is
![\frac{5}{8}x=\frac{7}{10} x-3\\ \\\frac{7}{10} x-\frac{5}{8} x=3\\](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B8%7Dx%3D%5Cfrac%7B7%7D%7B10%7D%20x-3%5C%5C%20%5C%5C%5Cfrac%7B7%7D%7B10%7D%20x-%5Cfrac%7B5%7D%7B8%7D%20x%3D3%5C%5C)
![\frac{56x-50x}{80} =3\\\\\\\frac{6}{80} x=3\\\\\\6x=80*3\\\\\\x=240/6\\\\x=40](https://tex.z-dn.net/?f=%5Cfrac%7B56x-50x%7D%7B80%7D%20%3D3%5C%5C%5C%5C%5C%5C%5Cfrac%7B6%7D%7B80%7D%20x%3D3%5C%5C%5C%5C%5C%5C6x%3D80%2A3%5C%5C%5C%5C%5C%5Cx%3D240%2F6%5C%5C%5C%5Cx%3D40)
So there were 40 sweets at first
Using the ratio of 7:3 then
Alice had 7/10 *40 = 28 sweets
Olivia had 3/10*40= 12 sweets
Alice gave Olivia 3 sweets, so she will remain with 28-3 =25 sweets. Olivia will now have 15 sweets.The new ratio will be 25:15 simplified as 5:3.
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Ratio : brainly.com/question/11095585
Keywords : Ratio
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