Sharing a sack of nuts.

A woman with four children bought a sack of peanuts. To the oldest child, a boy, she gave one peanut and 1/4 of what remained; and to each of the other children she did the same. (gave 1 peanut + 1/4 of the rest) The second child was a girl, the third a boy, and the last a girl. It was found that the boys had received 100 more peanuts than the girls.

What was the initial number of peanuts?

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