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!