### Brain Teasers

# Equations

What values of X and Y would make these equations work?

6751X + 3249Y = 26751

3249X + 6751Y = 23249

6751X + 3249Y = 26751

3249X + 6751Y = 23249

### Answer

Add the equations to give: 10000X + 10000Y = 50000Divide by 10000 to give: X + Y = 5

Subtract to give: 3502X - 3502Y = 3502

Divide by 3502 to give: X - Y = 1

Therefore: X = 3 and Y = 2

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## Comments

I really like this. It looks so scary but turns out to be fairly easy. If you spot that the two numbers addd to 10000 it helps. Great teaser!

I really like this. It looks so scary but turns out to be fairly easy. If you spot that the two numbers add to 10000 it helps. Great teaser!

how did you choose 50000?

Yeah, no need to use the equations to solve this one. The last four digits of each answer match the coefficient of x. That right there establishes that (x-1) = y and (x-1+y)/2 * (3249 + 6751) = 20000 which quickly leads (if not already noticed) that 3249 + 6751 = 10000. The rest is simple from there.

A few seconds in my head for the whole thing.

A few seconds in my head for the whole thing.

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