SOLUTION: when one− fourth of a number is added to one-seventh of the numberˏ the sum is 22 what is the number?

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Question 784739: when one− fourth of a number is added to one-seventh of the numberˏ the sum is 22 what is the number?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
MY WAY:
Obviously the number is a positive integer divisible by 4 and 7, so it's divisible by 4%2A7=28.
I can write the number as 28k, knowing that k is a natural number (positivw integer).
28k= the number
28k%2F4=7k= one-fourth of the number
28k%2F7=4k= one-seventh of the number
What the problem says in words is translated as
28k%2F4%2B28k%2F7=22 or 7k%2B4k=22
Solving:
28k%2F4%2B28k%2F7=22 --> 7k%2B4k=22 --> 11k=22 --> k=2 --> 28k=2%2A28 --> 28k=highlight%2856%29
If I do not have to explain my thinking, or "show my work", that is a fast way to solve the problem, and may help save time in a multiple choice test.

A MORE TRADITIONAL WAY:
N= the number
What the problem says in words is translated as
N%2F4%2BN%2F7=22
We multiply both sides times 4%2A7=28 to eliminate denominators
28%28N%2F4%2BN%2F7%29=28%2A22
28N%2F4%2B28N%2F7=618
7N%2B4N=618
11N=618
11N%2F11=618%2F11
N=highlight%2856%29