00:01
In this problem, it is said that a certain store has a number of bikes and tricycles for sale.
00:05
There are exactly 60 wheels altogether, and we need to determine how many bikes there are and how many tricycles there are.
00:12
Now, just this information alone is not enough to determine the exact number of bikes and the exact number of tricycles, but using the information given we can determine all of the possible options.
00:25
So how do we do that? let us consider b to be the number of bikes and t to be the number of bikes, and t to be the number of tricycles.
00:31
Now, each bike has two wheels, so 2b gives us the number of wheels on the bikes, and each tricycle has three wheels, so 3t gives us the number of wheels on the tricycles.
00:43
And if we add these two, we will have the total number of wheels in total, and that is given to be 60.
00:49
So b and t will be positive integers which are solutions to this equation.
00:57
So we can start plugging in values, suppose we take b to be 1, then we end up with 2 times 1 plus 3t is equal to 60, which means that 2 plus 3t is 60.
01:10
That means that 3t is 60 minus 2, which is 58, and that will imply that t is equal to 58 divided by 3, and this is not possible because this is not an integer, and we cannot have a fractional number of tricycles.
01:28
Now, let's suppose that instead of taking b as 1, we take b as 2.
01:35
Then what do we end up with, we have 2 times 2.
01:38
So now we have 4 over here.
01:42
And so 3t will be 60 minus 4 and that is equal to 56.
01:48
And so what we end up with is that t is equal to 56 divided by 3 and this still will not work because this is not an integer...