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# Black and Gold Storeys

**Answer:** 14

**Using reasoning**

**Using a table**

$25-a=25-b\therefore a=b$

$\therefore a=14$

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Age 11 to 14

ShortChallenge Level

- Problem
- Solutions

$25-a=25-b\therefore a=b$

**Using symbols for some of the numbers**

Gold storeys in top half: $x$

Black storeys in bottom half: $y$

Given that $x+y = 28$

Gold storeys in the bottom half: $25-x$

Black storey in the bottom half: $y$

$25-x+y=25 \Rightarrow x=y$

So $x+y=28$ means $x$ and $y$ are both $14$, since $x=y$

**Using symbols for all of the numbers**

$a$ gold storeys in the top half of the building.

$b$ gold storeys in the bottom half of the building.

$c$ black storeys in the top half of the building.

$d$ black storeys in the bottom half of the building.

Then:

$a+b$ = 25 (1)

$c+d$ = 25 (2)

$a+c$ = 25 (3)

$b+d$ = 25 (4)

$a+d$ = 28 (5)

(1) $-$ (4): $a+b-b-d$ = 0 $\Rightarrow a-d$ = 0 $\Rightarrow a$ = $d$

(5) becomes $a+a$ = 28, so $a$ = 14

You can find more short problems, arranged by curriculum topic, in our short problems collection.