Question 784739
MY WAY:
Obviously the number is a positive integer divisible by 4 and 7, so it's divisible by {{{4*7=28}}}.
I can write the number as {{{28k}}}, knowing that {{{k}}} is a natural number (positivw integer).
{{{28k}}}= the number
{{{28k/4=7k}}}= one-fourth of the number
{{{28k/7=4k}}}= one-seventh of the number
What the problem says in words is translated as
{{{28k/4+28k/7=22}}} or {{{7k+4k=22}}}
Solving:
{{{28k/4+28k/7=22}}} --> {{{7k+4k=22}}} --> {{{11k=22}}} --> {{{k=2}}} --> {{{28k=2*28}}} --> {{{28k=highlight(56)}}}
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/4+N/7=22}}}
We multiply both sides times {{{4*7=28}}} to eliminate denominators
{{{28(N/4+N/7)=28*22}}}
{{{28N/4+28N/7=618}}}
{{{7N+4N=618}}}
{{{11N=618}}}
{{{11N/11=618/11}}}
{{{N=highlight(56)}}}