I found this problem in a book that states it was set as a problem in the 3rd Junior International Mathematical Olympiad held in Hong-Kong in 1999. The hypothesis is as follows:
A furniture shop has sold 225 beds during the year 1998. At first, it sold 25 beds per month, then 16 beds per month, and finally 20 beds per month. For how many months has it been selling 25 beds per month?
I really like this problem. It is quite trivial yet may look a bit difficult at first. Here's my solution.
Based on the hypothesis, considering that:
x is the amount of months for which the shop had been selling 25 beds per month;
y is the amount of months for which the shop had been selling 16 beds per month;
z is the amount of months for which the shop had been selling 20 beds per month;
we can create the following system of equations:
which has (x,y,z)=(1,5,6) as a solution in the set of natural numbers.
A furniture shop has sold 225 beds during the year 1998. At first, it sold 25 beds per month, then 16 beds per month, and finally 20 beds per month. For how many months has it been selling 25 beds per month?
I really like this problem. It is quite trivial yet may look a bit difficult at first. Here's my solution.
Based on the hypothesis, considering that:
x is the amount of months for which the shop had been selling 25 beds per month;
y is the amount of months for which the shop had been selling 16 beds per month;
z is the amount of months for which the shop had been selling 20 beds per month;
we can create the following system of equations:
which can be written as:
which is equivalent to the following system:
In conclusion, the amount of months for which the shop had been selling 25 beds per month was equal to 1.
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