A word problem.

Question

A card collection was divided among Michelle and her three brothers. Armand received 1/3 of the cards. Ben received 1/4 of the cards, and Denis received 1/6 of the cards. Michelle received 345 cards. How many cards were in the collection before it was divided?

Answer 1

Let the x be the total number of cards before dividing.

 

Michelle has 345 cards.

Armand has 1/3 of the total number of cards: meaning Armand has 1/3*x cards.

Ben has 1/4 of the total number of cards: meaning Ben has 1/4*x cards.

Denis has 1/6 of the total number of cards: meaning Denis has 1/6*x cards.

 

Now, the total of number of cards these guys have must be equal to x (total number of cards before dividing). So:

 

345+1/3*x+1/4*x+1/6*x=x

 

Multiplying both sides by 12 (which is the greatest common devisor of 3, 4, and 6), we have:

 

12*345+4*x+3*x+2*x=12*x

 

Solving for x:

3*x=12*345 ==> x=1380 cards