Question 1190212
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You have 2 positive numbers. One number is one-fifth of the other number. 
The difference between the two numbers is 284, find the numbers.
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<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Algebra solution</H3>


The numbers are &nbsp;x &nbsp;and &nbsp;5x.


Their difference is &nbsp;284:


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5x - x = 284


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;4x   &nbsp;&nbsp;&nbsp;&nbsp;= 284


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x   &nbsp;&nbsp;&nbsp;&nbsp;= 284/4 = 71.


<U>ANSWER</U>.  &nbsp;&nbsp;&nbsp;&nbsp;The numbers are &nbsp;71 &nbsp;and &nbsp;5*71 = 355.


Solved.


<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Mental solution</H3>


The difference of &nbsp;284 &nbsp;is &nbsp;4/5 &nbsp;of the greater number.


Hence, &nbsp;1/5 &nbsp;of the greater number is &nbsp;1/4 &nbsp;of &nbsp;284, &nbsp;or &nbsp;71.


It means that the greater number is &nbsp;355 &nbsp;and the smaller number is &nbsp;355:5 = 71.


You get the same answer.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solved twice . . . 



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