Answer:
112 candies
Step-by-step explanation:
Start from the end.
Joe gave 25% of the remaining candies to his sister and has 21 candies left. Then
[tex]21 \ candies - 75\%\\ \\x \ candies - 25\%[/tex]
Write a proportion:
[tex]\dfrac{21}{x}=\dfrac{75}{25}\\ \\75x=21\cdot 25\\ \\x=\dfrac{21}{3}=7[/tex]
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,
[tex]28\ candies - \dfrac{2}{6}\\ \\x\ candies - \dfrac{4}{6}[/tex]
Write a proportion:
[tex]\dfrac{28}{x}=\dfrac{\frac{2}{6}}{\frac{4}{6}}\\ \\\dfrac{28}{x}=\dfrac{1}{2}\\ \\x=28\cdot 2=56[/tex]
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,
[tex]x\ candies - \dfrac{1}{4}\\ \\84\ candies - \dfrac{3}{4}[/tex]
Write a proportion:
[tex]\dfrac{x}{84}=\dfrac{\frac{1}{4}}{\frac{3}{4}}\\ \\\dfrac{x}{84}=\dfrac{1}{3}\\ \\3x=84\\ \\x=28[/tex]
Therefore, initially, Joe had 28 + 84 = 112 candies.
