How many tents were there at start?

Question

On an adventure trip the participants should stay in large tents. In each tent there are 12 beds. It was planned that if all tents of the same size were used and evenly used, a sleeping place would be left free in each tent.
When setting up the tents, however, you notice that 2 tents have been packed less than planned. Therefore it has now 7 sleeping places too little, although each sleeping place is used.

Answer 1

Let x = the planned number of tents

 

Translate:

"each tent there are 12 beds ... all tents of the same size ... evenly used, a sleeping place ... free in each tent"  means

    11 people in each tent

 

So, they planned x tents for 11x people.

 

"2 tents have been packed less than planned"    means (x-2) actual tents

"7 sleeping places too little, although each sleeping place is used"   means

        7 + (number of actual beds) = number of people

        7 +          12(x-2)                =    11x

 

The math:

        7 + 12x - 24 = 11x

         x = 17

  There were 17 tents planned.

 

Check:

   17 tents with 1 bed empty in each tent means 17*11 = 187 people

   15 full tents house 12*15=180, which is 7 beds too few.

      

Answer 2

Hi Mark and Anoushka, it would appear that the total number of tents originally planned was 17, but only 15 were provided.

 

Reason:

 

If all of the tents were provided, there would be 17 empty bunks. Since there were two missing tents, which should have held 22 places to sleep, you have to provide for the 22 missing places.

 

Each of the 15 tents provided would fill up using 15 of the missing 22 places, leaving 7 places unaccounted for.

 

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