A grandfather went to pick mushrooms in the forest with his four grandchildren. In the forest they dispersed and began searching. After a while the grandfather had 45 mushrooms and none of his grandchildren had managed to find even one.

The grandfather distributed all his mushrooms among the grandchildren who again looked for while the grandfather took a nap under a tree.

In the end, one of the children found two more mushrooms, another lost 2, the third found as many as mushrooms the grandfather had given him, and the fourth lost half of the mushrooms he received from the grandfather.

Upon returning home and counting the mushrooms they found that all the children had the same number of mushrooms in their basket.

**How many mushrooms did each child receive from grandfather and how many did each one have when they returned home?**

#### Solution

The first grandson received 12 mushrooms and lost 2 so he had 10 left when he got home.

The second grandson received 8 mushrooms and found 2 more so when he got home he had 10.

The third grandson received 5 mushrooms and found 5 more so he had 10 when he got home.

The room received 20 mushrooms and lost half so they came home with 10 mushrooms.

In total, 12 + 8 + 5 + 20 = 45 are the mushrooms that the grandfather initially found.