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Hi. Here's a math problem: (from my cet reviewer)

Jane had only 100 candies left after giving some of them to her playmates. She gave ⅙ to Catherine, ⅖ to Pat, and 20 pieces to Wendy. how many candies did jane originally have?

The equation in the book is:

x(1-(⅙))(1-(⅖))-20=100

Can you explain why that is the equation instead of:

x-(x/6)-(2x/5)-20=100

I asked Chat GPT and it says that my equation is the accurate one, not the equation provided by the book.​

Sagot :

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Now, let's simplify further:

[tex][x(1-(1/6))] - [((2/5)x(1-(1/6)))] = 100 + 20[/tex]

[tex][x(5/6)] - [(2/5)x(5/6)] = 120[/tex]

[tex]x(5/6)][1-(2/5)] = 120[/tex]

[tex]x(5/6)][1-(2/5)] = 120[/tex]

[tex][x(5/6)][3/5] = 120[/tex]

Divide both sides by (3/(5×6)) or (3/(30)) or (1/(10)):

[tex]x = 120 × (10)[/tex]

[tex]x = \boxed{1200}[/tex]

So, Jane originally had 1200 candies.