00:00When three interlocking gears rotate, the smallest one rotates 100 times, the largest one rotates 60 times, and the third one rotates 75 times.
00:06The question asks: If the diameter of the largest gear is 16 cm greater than the diameter of the smallest gear, what is the diameter of the other gear?
00:14Friends.
00:14Now, friends, in multiplication tables, if two identical multipliers are working together, the larger one will rotate less, so the number of rotations is inversely proportional to the multiplier.
00:32So it's in a multiplication situation.
00:33That's equal to k, which we'll call a constant of proportionality.
00:35In this case, based on the given information, we need to find the smallest common multiple of 100 revolutions, 60, and 75.
00:47In other words, in their cakes.
00:54That's quite likely, folks.
00:57Instead of doing it in a long way, it comes out as 300.
01:00So, it means we need to choose our proportionality constant such that it is a multiple of 300.
01:06As the smallest of the common floors.
01:09In this case, we say if 300 times k is chosen.
01:17Here's how it happens, folks.
01:20What was 100 times x, guys?
01:24The number of revolutions is one hundred, let's call the first one multiplied by the first one's diameter x.
01:28In the second case, I equate 75 times y, and in the third case, 60 times z, all equal to 300 times k.
01:38Here's our ratio, folks.
01:40What happens to our X here, guys?
01:42If we divide both sides by 100, we get 3k here.
01:45If we divide Y by 75 here, we get 4k.
01:50We find our Z to be 5k from this.
01:53And he asked us, "Friends, what is the largest multiplication of the diameter? What is the largest multiplication, friends?"
02:00Of course, it's z, right guys?
02:02Let's write it down like this.
02:05Z minus x, the smallest product of which is the diameter.
02:09It was 16 centimeters too much.
02:12So the difference is 16 centimeters.
02:14In this case, the question asks for the diameter of the other factor, which is the median factor.
02:19Let's find it right away.
02:20Let's replace Z with 5 times k, minus 3 times k, which equals 16.
02:26From our equation, 2 times k equals 16.
02:29We can therefore find our K to be equal to 8.
02:32So, what was our median product, guys?
02:34Y equals 4k.
02:38That's equal to 4 times 8, which equals 32 centimeters for the diameter.
02:43Our answer is Ceyhan.
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