# mensateaser [level 0] (part 1)

What should be the value of the bottom row in our

Euro 2012 Football themed grid?

• Er, not that I'm not grateful, but Glorfindel had the correct answer first, and the reasoning was okay. I just pointed out how it's a mathematical problem. He should get the accepted answer bonus, not me. – Josh Aug 10 '15 at 7:19

Glorfindel is correct, but there's an algebraic approach to it.

Let the shirt be x, the shorts be y, and the ball be z.

With that in mind, we now have:

2x + 2y = 100

3x + z = 145

x + y + 2z = 100

2x + y + z = ??

Now, we can solve for two variables, then use the substitution method. Taking the easiest, we get:

2x + 2y = 100 -> 2y = -2x + 100 -> y = -x + 50

3x + z = 145 -> z = -3x + 145

x + (-x + 50) + 2(-3x + 145) = 100

This equates out to:

x - x + 50 - 6x + 290 = 100 -> 50 - 6x + 290 = 100 -> -6x + 340 = 100 -> -6x = -240 -> x = 40

Now that we know what x is, we can solve the rest.

2(40) + 2y = 100 -> 80 + 2y = 100 -> 2y = 20 -> y = 10

40 + 10 + 2z = 100 -> 50 + 2z = 100 -> 2z = 50 -> z = 25

2(40) + 10 + 25 = 115

This was more a mathematical problem than a puzzle, though.