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?
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
Each lost X keys.
541-x = 6(316 - x).
541 - x = 1896 - 6x,
6x-x = 1896 - 541,
5x = 1355,
X = 271 Keys.
To solve this problem, let's first set up an equation based on the information given. Let's say both Marty and Nick lost the same number of keys, represented by 'x'.
After losing 'x' keys, Marty had 316 - x keys, and Nick had 541 - x keys. According to the problem, Nick had 6 times as many keys as Marty, so we can write the following equation:
541 - x = 6(316 - x)
Now, we can solve this equation to find the value of 'x', representing the number of keys they both lost.
541 - x = 1896 - 6x
Combining like terms, we have:
5x = 1896 - 541
5x = 1355
Dividing both sides of the equation by 5, we get:
x = 1355 / 5
x = 271
So, both Marty and Nick lost 271 keys each.