Question 890201
{{{(matrix(4,1,
Number,of,LARGE,buses))}}}{{{TIMES}}}{{{(matrix(7,1,

Number,of,seats,on,a,LARGE,bus))}}}{{{PLUS}}}{{{(matrix(4,1,
Number,of,SMALL,buses))}}}{{{TIMES}}}{{{(matrix(7,1,

Number,of,seats,on,a,SMALL,bus))}}} {{{EQUALS}}} {{{(matrix(9,1,
The,total,number,of,seats,on,all,the,buses))}}}
</pre>
There are 4 large buses 
<pre>
Number of LARGE buses = 4
</pre>
and 5 small buses. 
<pre>
Number of SMALL buses = 5
</pre>
The large buses have 12 more seats than the smaller buses. 
<pre>
Number of seats on a LARGE bus = WE DON'T KNOW!

Number of seats on a SMALL bus = WE DON'T KNOW!

So we have to let one of these equal to an unknown letter,

Since this sentence:
</pre>
The large buses have 12 more seats than the smaller buses.
<pre>
defines the number of seats on the LARGE buses in terms of the number
of seats on the SMALL buses, we let the letter N represent the second
one, the number of seats on a SMALL bus.

Number of seats on a SMALL bus = N

This sentence:
</pre>
The large buses have 12 more seats than the smaller buses.
<pre>
tells us that we would add 12 to N to get the number of seats on a
LARGE bus, so we add 12 to N, and get:

Number of seats on a LARGE bus = (N+12)
</pre>
There are 336 seats total.
<pre>
So the total number of seats on all the buses = 336.

So we have:

{{{(matrix(6,1,
Number,of,LARGE,buses,"THAT'S",4))}}}{{{TIMES}}}{{{(matrix(9,1,

Number,of,seats,on,a,LARGE,bus,"THAT'S",(N+12)))}}}{{{PLUS}}}{{{(matrix(6,1,
Number,of,SMALL,buses,"THAT'S",5))}}}{{{TIMES}}}{{{(matrix(9,1,

Number,of,seats,on,a,SMALL,bus,"THAT'S",N))}}} {{{EQUALS}}} {{{(matrix(11,1,
The,total,number,of,seats,on,all,the,buses,"THAT's",336))}}}

          4(N+12) + 5N = 336

Use the distributive principle to remove the parentheses:

            4N+48 + 5N = 336

Combine like terms 4N and 5N getting 9N

               9N + 48 = 336

Subtract 48 from both sides:

                    9N = 288

Divide both sides by 9

                   {{{9N/9}}} = {{{288/9}}}

Cancel the 9's anddivide 288 by 9

                                <u>  32</u>
                            N = 9)288  
                                 <u>27</u>
                                  18
                                  <u>18</u>

                            N = 32

Number of seats on a SMALL bus = N = 32

Number of seats on a LARGE bus = (N+12) = (32+12) = 44

-----

Checking:  5 SMALL busses times 32 seats = 5×32 = 160
           4 LARGE busses times 44 seats = 4×44 = 176
                               TOTAL SEATS      = 336

That checks, so we are right.

Edwin</pre>