Subject: Math
Name: Cathey
Who are you: Parent (Secondary)

Four children are playing with marbles. At the end of the day, one child has four less than half the marbles. The second child has six more than one-fifth the marbles. The third child has one third of what the first child has and the fourth child has one less than the third child. How many marbles are there?


Hi Cathey. You can use algebra to solve this problem.

Let M = the total number of marbles of all the children combined.

Then the first child has (1/2)M - 4 marbles.
The second child has (1/5)M + 6 marbles.
The third child has (1/3)( (1/2)M - 4) marbles.
The fourth child has ( (1/5)M + 6 ) - 1 marbles.
We can add up these totals in two ways. The simple way is just to
say that the total is M, as we decided in the beginning. The other
way is to add up each child's marble count. Since these two
quantities must be the same, they equal each other. So:

M = ( (1/2)M - 4 ) + ( (1/5)M + 6) + ( (1/3) ( ( 1/2) M - 4) ) + ((1/5)M + 6 ) - 1.

If you simplify this equation, you can "solve for M" and get the answer to your question.

Hope this helps,
Stephen La Rocque.