Please explain how you get your answer Problem Solving Appli

Please explain how you get your answer.

Problem Solving Application: On her way home from school Gloria Sol met a friend and gave her one half of all her candy. Next, she met another friend and gave her one third of all the candy she had left. Then, she met another friend and gave him one half of all the candy she had left. She then had 9 pieces left. How many pieces did she start with?

Solution

Let Gloria has \"x\" candy

she gave one-half to her friend = 1/2 *x

candies left with her = (x - x/2)

she met another friend and gave one-third of the candies she have = 1/3 *(x-x/2)

candies left with her = (x - x/2) - 1/3 (x - x/2)

she gave half of the candies left to another friend = 1/2 * [(x-x/2) -1/3 (x-x/2)]

candies left with her = (x - x/2) - 1/3 (x - x/2) - 1/2 * [(x-x/2) -1/3 (x-x/2)]

she has 9 pieces left

(x - x/2) - 1/3 (x - x/2) - 1/2 * [(x-x/2) -1/3 (x-x/2)] = 9

(2x-x)/2 -1/3(2x-x)/2 -1/2 [x/2 -x/6] = 9

x/2 -x/6 -1/2[2x/6] = 9

3x/6 -x/6 -x/6 =9                   // we have to make the same denominator

(3x-x-x)/6 = 9

x/6 = 9

x = 54

therefore initially she had 54 candies