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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

User MathiasJ
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4 votes

Answer:

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.

User Hayesgm
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