How many buses does this company currently own?

My local bus company has recently expanded and no longer has enough room for all of its buses.

Twelve of their buses have to be stored outside.

If they decide to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future.

How many buses does the company currently own?

 

 

 

 

 
Answer: 72 buses.

They have enough room for 60 of these, expanding the 60 capacity by 40% will give them enough room for 84, which we know is 12 more spaces than they currently need.
If they have B buses and S spaces before the expansion, they have enough room for:

S = B – 12 [1]

After the expansion they have more spaces, and enough room for:

S + 0.4 x S = B + 12 [2]

Rewriting [2] as:

1.4S = B + 12

and again as

B = 1.4S – 12 [3]

We can rewrite [1] as:

B = S + 12 [4]

Making [3] = [4] we have:

1.4S – 12 = S + 12

Subtracting S from both sides gives:

0.4S – 12 = 12

Adding 12 to both sides gives:

0.4S = 24

Multiplying by 10 and dividing by 4 on both sides gives:

S = 60

Using S = 60 in [4] gives B = 72.

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