SOLUTION: There are 4 large buses and 5 small buses. The large buses has 12 more seats than the smaller buses. There are 336 seats total? How many more seats are on the large buses?

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Question 890201: There are 4 large buses and 5 small buses. The large buses has 12 more seats than the smaller buses. There are 336 seats total? How many more seats are on the large buses?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%28matrix%284%2C1%2C%0D%0ANumber%2Cof%2CLARGE%2Cbuses%29%29TIMES%28matrix%287%2C1%2C%0D%0A%0D%0ANumber%2Cof%2Cseats%2Con%2Ca%2CLARGE%2Cbus%29%29PLUS%28matrix%284%2C1%2C%0D%0ANumber%2Cof%2CSMALL%2Cbuses%29%29TIMES%28matrix%287%2C1%2C%0D%0A%0D%0ANumber%2Cof%2Cseats%2Con%2Ca%2CSMALL%2Cbus%29%29 EQUALS %28matrix%289%2C1%2C%0D%0AThe%2Ctotal%2Cnumber%2Cof%2Cseats%2Con%2Call%2Cthe%2Cbuses%29%29

There are 4 large buses 
Number of LARGE buses = 4

and 5 small buses. 
Number of SMALL buses = 5

The large buses have 12 more seats than the smaller buses. 
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:

The large buses have 12 more seats than the smaller buses.
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:

The large buses have 12 more seats than the smaller buses.
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)

There are 336 seats total.
So the total number of seats on all the buses = 336.

So we have:

%28matrix%286%2C1%2C%0D%0ANumber%2Cof%2CLARGE%2Cbuses%2C%22THAT%27S%22%2C4%29%29TIMESPLUS%28matrix%286%2C1%2C%0D%0ANumber%2Cof%2CSMALL%2Cbuses%2C%22THAT%27S%22%2C5%29%29TIMES EQUALS 

          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%2F9 = 288%2F9

Cancel the 9's anddivide 288 by 9

                                  32
                            N = 9)288  
                                 27
                                  18
                                  18

                            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