SOLUTION: The sum of two numbers is 47. The sum of the smaller and 2 times the larger is 76 . Find the numbers?

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Question 1100983: The sum of two numbers is 47. The sum of the smaller and 2 times the larger is 76 . Find the numbers?
Found 3 solutions by josgarithmetic, addingup, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x%3Cy

system%28x%2By=47%2Cx%2B2y=76%29

x can be "eliminated" to first find y value.
Do you understand how y=76-47 ?
-
%28x%2B2y%29-%28x%2By%29=76-47
x%2B2y-x-y=29
x-x%2B2y-y=29
y=29-------and then use this to evaluate x.

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
x+y = 47
x+2y = 76
47-y+2y = 76
y = 29
76-58 = 18
x = 18
-------------------------------
check
18+29 = 47
18+2*29 = 76
Correct.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


You can solve this without algebra, by using logical reasoning.

The first sum is the sum of each of the two numbers once; the second sum is different only in that the second number is added twice.

So the difference between the two sums is the second number.

76-47 = 29, so the second number is 29.

Then the first number is 47-29 = 18.

The algebraic solution does exactly the same thing as this informal solution. So you should learn the formal process for solving problems like this using algebra; but you should also try to get some exercise in logical reasoning by solving the problem without the formal methods.

Here is an algebraic solution:

x%2By+=+47
x%2B2y+=+76
y+=+29 (subtract the first equation from the second)
x+=+47-29+=+18

You can see that, in this case, the steps of the formal solution are exactly the same as the steps of the informal solution.