Question 564052: I am not sure what topic this question would fall under since i didn't find word problems under the algebra stuff. sorry. anyways i have been working on 4 questions for the last 2 months and i just cannot figure it out so maybe you can help.
a company has four large buses and five small ones. Each large bus has 12 seats more than a small bus. The total seating capacity of all buses is 336. how many seats are on a large bus?
Thanks in advance)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The best way to solve the problem depends on why you need the answer. If it's homework for an algebra class and you need to "show your work", you want to do it algebra-style, with few words, just symbols and variables. For a real life situation, or a test requiring just the solution, without explanations, without "showing your work", you can solve this problem without even thinking of algebra. Explaining the reasoning takes a few sentences, and slows you down a bit.
WITHOUT INVOKING ALGEBRA
You could say that if all the buses were small you would have 48 seats less (4 large buses times 12 extra seats per large bus is 48 extra seats). Then you would have 336-48=288 seats from 9 small buses. That would mean 32 seats per small bus (288 divided by 9 is 32). A large bus seating capacity would then calculate as 12+32=44.
Each large bus has 44 seats.
THE ALGEBRA APPROACH (explanations that you would not necessarily write for homework are in parenthesis).
Let S be the number of seats in each small bus.
Let L be the number of seats in each large bus.
(We know that a large bus seats 12 more passengers, so)
L=S+12
(The number of seats in the 4 large buses is 4L, 4 times L.
The number of seats in the 5 small buses is 5S, 5 times S.
We know that the total number of seats is 366, so)
4L+5S=366
We have a system of two linear equations with two variables:
We solve it by substitution
Substituting into we get
 --> 
Each large bus has 44 seats.
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