Question 271152
If the larger of two numbers is divided by 6 and is subtracted from three times the smaller number, the result is 44. If the smaller number is increased by 4, the result is half the largest number.

<pre><font size = 4 color = "indigo"><b>

The other tutor just gave you the equations and solved them.  I think
your problem is not as much solving the equtions so much as getting
them from the words.  I will show you how to get the equations from
the words.

In the following, observe what I have substituted the <font color ="red">red</font> parts
for from one sentence to the next, and you'll see how the equations
come from the words:

If <font color = "red">the larger of two numbers</font> is divided by 6 and is subtracted from three
times the smaller number, the result is 44. If the smaller number is increased
by 4, the result is half the largest number.

If <font color = "red">L</font> is divided by 6 and is subtracted from three times the smaller number,
the result is 44. If the smaller number is increased by 4, the result is half
the largest number.

<font color = "red">If L is divided by 6 and</font> is subtracted from three times the smaller number,
the result is 44. If the smaller number is increased by 4, the result is half
the largest number.

<font color = "red">L/6</font> is subtracted from three times the smaller number, the result is 44. If
the smaller number is increased by 4, the result is half the largest number.

L/6 is subtracted from three times <font color = "red">the smaller number</font>, the result is 44. If
the smaller number is increased by 4, the result is half the largest number.

L/6 is subtracted from three times <font color = "red">S</font>, the result is 44. If the smaller number
is increased by 4, the result is half the largest number.

L/6 is subtracted from <font color = "red">three times S</font>, the result is 44. If the smaller number
is increased by 4, the result is half the largest number.

L/6 is subtracted from <font color = "red">3S</font>, the result is 44. If the smaller number is
increased by 4, the result is half the largest number.

<font color = "red">L/6 is subtracted from 3S</font>, the result is 44. If the smaller number is
increased by 4, the result is half the largest number.

<font color = "red">3S MINUS L/6</font>, the result is 44. If the smaller number is increased by 4, the
result is half the largest number.

<font color = "red">3S - L/6</font>, the result is 44. If the smaller number is increased by 4, the
result is half the largest number.

3S - L/6<font color = "red">, the result is</font> 44. If the smaller number is increased by 4, the
result is half the largest number.

3S - L/6 <font color = "red">=</font> 44. If the smaller number is increased by 4, the result is half the
largest number.

3S - L/6 = 44. If <font color = "red">the smaller number</font> is increased by 4, the result is half the
largest number.

3S - L/6 = 44. If <font color = "red">S</font> is increased by 4, the result is half the largest number.

3S - L/6 = 44. <font color = "red">If S is increased by 4</font>, the result is half the largest number.

3S - L/6 = 44. <font color = "red">S PLUS 4</font>, the result is half the largest number.

3S - L/6 = 44. <font color = "red">S + 4</font>, the result is half the largest number.

3S - L/6 = 44. S + 4, the result is half <font color = "red">the largest number</font>.

3S - L/6 = 44. S + 4, the result is half <font color = "red">L</font>.

3S - L/6 = 44. S + 4, the result is <font color = "red">half</font> L.

3S - L/6 = 44. S + 4, the result is <font color = "red">(1/2)</font> L.

3S - L/6 = 44. S + 4, the result is <font color = "red">(1/2) L</font>.

3S - L/6 = 44. S + 4<font color = "red">, the result is</font> (1/2) L.

3S - L/6 = 44. S + 4 <font color = "red">=</font> (1/2) L.

So we have the system of equations:

{{{system(3S - L/6 = 44, S + 4 = (1/2) L)}}}

Multiply the first equation through by 6 to clear of fractions:
Multiply the second equation through by 2 to clear of fractions:

{{{system(18S - L = 264, 2S + 4=  L)}}}


Multiply the first equation through by 6 to clear of fractions:
Multiply the second equation through by 2 to clear of fractions:

{{{system(18S - L = 264, 2S + 8=  L)}}}

Substitute {{{(2S + 8)}}} for L in the first equation:

{{{18S - (2S+8) = 264}}}

{{{18S - 2S-8 = 264}}}

{{{16S = 272}}}

{{{S=272/16}}}

{{{S=17}}}

Substitute 17 for S in

{{{2S + 8=  L)}}}

{{{2(17) + 8=  L)}}}

{{{34 + 8=  L)}}}

{{{42=L}}}

So the smaller number is 17 and the larger number is 42.

Edwin</pre>