90% FAILED to Solve this Math Puzzle

Today, we'll be working on this fun little puzzle. The goal is to fill in four boxes with numbers such that, when we perform simple math operations on them, we get specific results. 21, 9, 5, and 8, like this. Sounds interesting, right? So, how to solve it? The very first thing that should come to our mind is to label the boxes as variables, so that we can form equations and solve them step by step. Okay, so let's label the boxes as P, Q, R, and S, like this. Now, what to do? Let's try to make some equations using these boxes. Maybe start by looking at rows and columns and see what operations we can use. Look at this first row. We are told that P times Q is 21. Now, look at the second row. We are told that R minus S is 5. Great! That gives us two equations already. Now, move to the first column going down. P plus R is 8. And finally, look at the second column going down. Q times S is 9. Wow! So now we have four equations and four unknowns, which means we can solve this. Let us see how we can solve them step by step. Let's begin with the second and third equations. From R minus S equal to 5 and P plus R equal to 8. If we subtract the second equation from the third, we get P plus R minus R plus S, which simplifies to P plus S. And on the right side, 8 minus 5 gives us 3. So now we have P plus S equals 3. Let's keep that aside. Now take the first equation, P times Q equals 21, and divide both sides by P to get Q equals 21 divided by P. Similarly, from the last equation, Q times S equals 9, we divide both sides by S to get Q equals 9 divided by S. Since both are equal to Q, we can set them equal to each other. So 21 divided by P equals 9 divided by S. Now cross-multiplying, we get 21 times S equals 9 times P. Let's isolate P by dividing both sides by 9, giving us P equals 21 times S divided by 9. Now we substitute this expression of P into the earlier equation, P plus S equals 3. That gives us 21 times S divided by 9 plus S equals 3. To simplify this, make both terms have a denominator of 9. So the first term remains 21 times S over 9, and the second becomes 9 times S over 9. Adding them gives 30 times S over 9 equals 3. Now, multiplying both sides by 9, we get 30 times S equals 27. So S equals 27 divided by 30, which is 0.9. Now substitute this back to find P. So P equals 21 times 0.9 divided by 9, which gives us P equals 2.1. Now use this to find R, since P plus R is 8. We have 2.1 plus R equals 8, so R equals 8 minus 2.1, which is 5.9. Finally, we can find Q using the first equation. So Q equals 21 divided by 2.1, which is 10. And that's it. We have our value. So good.