## Thursday, February 28, 2013

### Word Problem - Partition, Distribution

Category: Algebra

"Published in Newark, California, USA"

Alberto would like to distribute a bagful of marbles equally among his friends. He figures out that if he were to give them 7 marbles each, he will need 4 marbles more but if he were to give them 6, he will have 3 marbles left. How many marbles does Alberto have?

Solution:

For this type of word problem, we will use the principles of linear equation where the partition or distribution of items is involved. Let's analyze the given word problem as follows

Let x be the number of marbles
y be the number of friends to distribute the marbles

If the statement says "if he were to give them 7 marbles each, he will need 4 marbles more", then the working equation will be

or

If the statement says "if he were to give them 6, he will have 3 marbles left", then the working equation will be

or

Equate x = x, we have

Therefore,

Substitute the value of y to either one of the two equations, we have

Therefore, Alberto has 294 marbles that he distributed to his 46 friends