```Question 91629
Let's begin by calling the smaller number S and the larger number L.
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The problem tells you that the sum of these two numbers is 36. Therefore, we can write the
equation:
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{{{S + 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/S}}}
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Furthermore it tells you that the result of this division equals 2 plus a remainder of
{{{3/S}}}
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So the equation form of this division is:
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{{{L/S = 2 + 3/S}}} <=== 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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{{{(36 - S)/S = 2 + 3/S}}}
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Notice that if we say the first term on the right side (that term is 2) is equivalent to
{{{2S/S}}} then we can substitute {{{2S/S}}} for 2 and every term in the equation will
then have an S in the denominator and the equation will be:
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{{{(36 - S)/S = 2S/S + 3/S}}}
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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 + 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 + 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 = 33/3 = 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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