# 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 ->  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

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 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 questionAnswer by bucky(2189)   (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: . <=== first equation . The the problem tells you to divide the larger number by the smaller number. In algebraic form this would be . Furthermore it tells you that the result of this division equals 2 plus a remainder of . So the equation form of this division is: . <=== second equation . If we return to the first equation and subtract S from both sides, we get: . . Since L equals 36 - S we can substitute 36 - S for L in the second equation which then becomes: . . Notice that if we say the first term on the right side (that term is 2) is equivalent to then we can substitute for 2 and every term in the equation will then have an S in the denominator and the equation will be: . . We can now get rid of the S in the denominator by multiplying all terms on both sides by S to get: . . Now add S to both sides of the equation to get rid of the -S on the left side. The equation then becomes: . . Then subtract 3 from both sides to get rid of the 3 on the right side. The equation then becomes: . . Finally, divide both sides by 3 to solve for S: . . 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. . So the two numbers are 11 and 25. . Check: is their sum 36? Yes it is. . 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. . Hope this helps you to see your way through the problem. .