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Black and Gold Storeys

Age 11 to 14 Short
Challenge Level

Answer: 14


Using reasoning
 




Using a table
            

$25-a=25-b\therefore a=b$
 
 $\therefore a=14$


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.