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Hi..I have trouble creating equations to solve problems such as the one below.

Jim has 94 marbles and Mary has 80 marbles. How many marbles must Mary give to Jim so that Jim now has 40 marbles more that Mary?

Are there some easy ways to make my students solve this type of problem?

regards

roy

To solve, go over the facts given.

Since Jim has 94 marbles and Mary has 80 marbles,

the current difference is 94 - 80 = 14.

For each marble given, this increase the difference by 2

since Jim increases by one for each marble and Mary decreases by 1.

For example, if only 1 marble is given away, that makes the new numbers 94+1 = 95

and 80-1 = 79, and 95-79 = 16, which is 14+2.

The difference wanted is 40, and the current difference is 14.

Taking the difference gives the amount of change necessary.

That is, 40 - 14 = 26, and that's the amount of change from what we have now that's needed.

Since each marble makes a change of 2, 26/2 = 13,

and this means 13 more marbles need to change hands.

This gives Jim 94 + 13 = 107 and Mary 80 - 13 = 67.

As can be seen, 107 - 67 = 40, and that's what we want.

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