Marty had 316 keys and Nick had 541 keys. After both of them lost the same number of keys, Nick had 6 times as many keys as Marty. How many keys did each of them lose?

Answer 1

If they both lost x keys, then
541-x = 6(316-x)
541-x = 1896-6x
5x = 1355
x = 271

check:
316-271 = 45
541-271 = 270 = 6*45

Answer 2

Each lost X keys.
541-x = 6(316 - x).
541 - x = 1896 - 6x,
6x-x = 1896 - 541,
5x = 1355,
X = 271 Keys.