Question 44: The number of marbles of three friends Minh, Hung, Dung is proportional to the numbers \(2; 4; 5.\) Calculate the number of marbles for each of you, knowing that the three of you have all \(44\) marbles .

Let the number of marbles of three friends Minh, Hung, Dung be \(x, y, z\) \((x,y,z \in\mathbb {N^*})\)

According to the problem, we have: \(\dfrac{x}{2}= \dfrac{y}{4} = \dfrac{z}{5}\) and \(x + y + z = 44\)

From there, applying the property of the series of equal ratios, we deduce:

\(\dfrac{x}{2}= \dfrac{y}{4} = \dfrac{z}{5}\) = \(\dfrac{x+y+z}{2+4+5} = \dfrac{44}{11} = 4\)

Therefore:

\( x =4.2=8\) (satisfied)

\( y = 4.4 = 16\) (satisfied)

\( z = 4.5= 20\) (satisfied)

So Minh has \(8\) marbles, Hung has \(16\) marbles, Dung has \(20\) marbles.

Answer: 8; 16; 20 marbles.