Question

Joe gave 1⁄4 of his total candies to his classmates. Then he gave 4/6 of what he had left to his brother when he went home. He then realized that he didn’t give any to his sister, so he gave 25% of the remaining candies to her. After all this, he realized he only had 21 candies left. How many candies did he have in the beginning

Answer 1

112 candies

Explanation:

Start from the end.

Joe gave 25% of the remaining candies to his sister and has 21 candies left. Then

`21 \ candies - 75\%\\ \\x \ candies - 25\%`

Write a proportion:

`(21)/(x)=(75)/(25)\\ \\75x=21\cdot 25\\ \\x=(21)/(3)=7`

Joe gave 7 candies to his sister, so before this he had 21 + 7 = 28 candies.

He gave 4/6 of what he had left to his brother when he went home, so 2/6 of all his candies left ot him. Hence,

`28\ candies - (2)/(6)\\ \\x\ candies - (4)/(6)`

Write a proportion:

`(28)/(x)=((2)/(6))/((4)/(6))\\ \\(28)/(x)=(1)/(2)\\ \\x=28\cdot 2=56`

Joe gave 56 candies to his brother, so Joe had 28 + 56 = 84 candies when he went home.

Joe gave 1/4 of his total candies to his classmates, so 3/4 of his candies left to him. So,

`x\ candies - (1)/(4)\\ \\84\ candies - (3)/(4)`

Write a proportion:

`(x)/(84)=((1)/(4))/((3)/(4))\\ \\(x)/(84)=(1)/(3)\\ \\3x=84\\ \\x=28`

Therefore, initially, Joe had 28 + 84 = 112 candies.