SOLUTION: I don't understand how to solve this complicated linear equation word problem. I would really appreciate if you could help me out, thanks. THE SUM OF TWO NUMBERS IS 36. IF THE L

Algebra ->  Linear-equations -> SOLUTION: I don't understand how to solve this complicated linear equation word problem. I would really appreciate if you could help me out, thanks. THE SUM OF TWO NUMBERS IS 36. IF THE L      Log On


   

Question 91629: I don't understand how to solve this complicated linear equation word problem. I would really appreciate if you could help me out, thanks.
THE SUM OF TWO NUMBERS IS 36. IF THE LARGER NUMBER IS DIVIDED BY THE SMALLER NUMBER, THE QUOTIENT IS 2 AND THE REMAINDER IS 3. FIND THE NUMBERS.
I'm sorry but this isn't a textbook question
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let's begin by calling the smaller number S and the larger number L.
.
The problem tells you that the sum of these two numbers is 36. Therefore, we can write the
equation:
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S+%2B+L+=+36 <=== first equation
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The the problem tells you to divide the larger number by the smaller number. In algebraic
form this would be L%2FS
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Furthermore it tells you that the result of this division equals 2 plus a remainder of
3%2FS
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So the equation form of this division is:
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L%2FS+=+2+%2B+3%2FS <=== second equation
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If we return to the first equation and subtract S from both sides, we get:
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L+=+36+-+S
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Since L equals 36 - S we can substitute 36 - S for L in the second equation which then
becomes:
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%2836+-+S%29%2FS+=+2+%2B+3%2FS
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Notice that if we say the first term on the right side (that term is 2) is equivalent to
2S%2FS then we can substitute 2S%2FS for 2 and every term in the equation will
then have an S in the denominator and the equation will be:
.
%2836+-+S%29%2FS+=+2S%2FS+%2B+3%2FS
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We can now get rid of the S in the denominator by multiplying all terms on both sides by S
to get:
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36+-+S+=+2S+%2B+3
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Now add S to both sides of the equation to get rid of the -S on the left side. The equation
then becomes:
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36+=+3S+%2B+3
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Then subtract 3 from both sides to get rid of the 3 on the right side. The equation
then becomes:
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33+=+3S
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Finally, divide both sides by 3 to solve for S:
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S+=+33%2F3+=+11
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So now we know the smaller number is 11. But since the sum of the two numbers is 36, then
the larger number must be 25 because 36 - 11 = 25.
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So the two numbers are 11 and 25.
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Check: is their sum 36? Yes it is.
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If you divide the larger (25) by the smaller (11) do you get an answer of 2 with a remainder
of 3? Yes you do. Our answer checks ... the smaller number is 11 and the larger number is 25.
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Hope this helps you to see your way through the problem.
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