SOLUTION: The sum of two numbers is 6. Five times the first number equals 10 times the second number. Find the two numbers .

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Question 1149486: The sum of two numbers is 6. Five times the first number equals 10 times the second number. Find the two numbers .
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52850)   (Show Source): You can put this solution on YOUR website!
.

Let first number be x.  Then the second number is (6-x), according to the condition.


Then you have this equation 


    5x = 10*(6-x).


Simplify and solve


    5x = 60 - 10x

    5x + 10x = 60

     x       = 60/15 = 4.


ANSWER.  First number is 4.  Second number is  (6-4) = 2.

Solved.


Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


If you are solving this problem in a basic algebra course, then you should fully understand the formal solution shown by the other tutor.

If you don't need a formal algebraic solution, logical reasoning and some very simple mental arithmetic will get to to the answer in very little time.

(1) If 5 times the first number is equal to 10 times the second, then the first number is 2 times the second.
(2) So now you have two numbers, one of which is twice the other, and their sum is 6. Simple reasoning quickly tells you the two numbers are 4 and 2.
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