Question

Find three conescutive whole numbers whose sum is more than $45$ but less the $54$.

Answer 1

Let $x$ be the smallest number.

The other $2$ numbers are $(x+1)$ and $(x+2)$.

Since,

The sum is more than $45$ but less that $54$

$45<x+(x+1)+(x+2)<54$

$45<x+x+1+x+2<54$

$45<3x+3<54$

$42<3x<51$

$42<3x<51$

$14<x<17$

So, the smallest number must be between $14$ and $17.$

Therefore,

The possible numbers are $15$ and $16.$

If $x=15$

$x+1=15+1=16$

$x+2=15+2=17$

Total sum $=15+16+17=48$

If $x=16$

$x+1=16+1=17$

$x+2=16+2=18$

Total sum $=16+17+18=51$

Hence, the two possible set of numbers are $15,16$ and $17$ or $16,17$ and $18$.