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:
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
=
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
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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