Question:
The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.
(a) 112
(b) 126
(c) 119
(d) 116
Solution:
(a) Let the three consecutive multiples of 7 be $7 x,(7 x+7),(7 x+14)$
where $x$ is a natural number.
According to the question,
$7 x+(7 x+7)+(7 x+14)=357$
$\Rightarrow \quad 21 x+21=357$
$\Rightarrow \quad 21(x+1)=357$
$\Rightarrow \quad \frac{21(x+1)}{21}=\frac{357}{21}$ [dividing both sides by 21 ]
$\Rightarrow \quad x+1=17$
$\Rightarrow \quad x=17-1 \quad$ [transposing 1 to RHS]
$\therefore \quad x=16$
Hence, the smallest multiple of 7 is $7 \times 16, i . \theta, 112$.