Thức khuya nhiều tổn hại sức khỏe đấy các cú đêm. Cô chúc cả nhà ngủ ngon!
I am an organizer of the Maths-English contest, so of course I'd love to answer these topics!
Calling the number of apples the sister left for her brothers x [apple(s), \(x\in N\)*].
With the first statement related to the question, the oldest brother divided the apples into three parts, leaving an apple to the youngest one. So the number of apples left for the two younger brothers is: \(\dfrac{x}{3}+\left(\dfrac{x}{3}+1\right)=\dfrac{2x+3}{3}\).
With the second statement, the middle brother divided the apples into three thirds and gave away one apple in his ration. So therefore, the number of apples left for the youngest brother is: \(\dfrac{\dfrac{2x+3}{3}}{3}+\left(\dfrac{\dfrac{2x+3}{3}}{3}+1\right)=2.\dfrac{2x+3}{9}+1=\dfrac{4x+6}{9}+1=\dfrac{4x+15}{9}\).
With the third statement, the youngest brother woke up and saw 7 apples. So we have:
\(\dfrac{4x+15}{9}=7\)
\(\Leftrightarrow4x+15=63\).
\(\Leftrightarrow4x=48\).
\(\Leftrightarrow x=12\). This answer satisfies the conditions of x.
Thanks everyone for your interest to this answer. And don't forget, the Vietnam English-Maths Contest hosted by me and VICE members will begin in the 29th of June, 2021 ^^
