The Weekly Warlock Wind-Up: Number 26 (answer)

This week I showed you this grid and asked you to calculate the value of the top row of the grid:

Find the solution after the break!

Okay so, hopefully you all realised, or at least guessed, two things – it’s going to require algebra, and the mathematical function is addition (for example, you would take the second row down as B + A + A + B = 100).  After that, there might be several different ways to work out the values of all the letters but the following is the way I did it:

Step 1 – Find the relationship between A and B

Looking at that second row, we see B + A + A + B = 100. This can also be written as 2A + 2B = 100.

Divide both sides of the equation by 2 to get A + B = 50.

Step 2 – Find A

Now we’re going to take the other of the equations which involves only A and B – the second column from the left. So 3A + B = 90.

Next we rewrite the equation we found first of all, to give us B = 50 – A.

Then we can substitute one equation into the other: 3A + (50 – A) = 90, which can be simplified down to 2A = 40.

This gives us A = 20.

Step 3 – Find B

We already know A + B = 50 and A = 20 so therefore B = 30.

Step 4 – Find C

To get a value for C, we can use the other equation given to us in the grid: A + B + 2C = 140.

By substituting in our values for A and B, we get 20 + 30 + 2C = 140, which can be simplified to 2C = 90.

Therefore C = 45.

Step 5 – Calculate the top row

Now that we have a value for every letter, let’s just put the numbers into the equation of the top row: A + 2B + C.

So, 20 + 60 + 45 = 125.

Seems like more folks got it right this week – I’ll have to toughen up again!



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