Question

2. The sum of two consecutive multiples of 7 is 189. The smaller multiple is​

Answer 1

Explanation:

$\textsf{\textbf{Given,}}$

The sum of two consecutive multiples of 7 have a sum of 189.

Let the smaller multiple be 7x. Then the other multiple is 7(x+1).

Therefore, we can form the following equation:

$\mathsf{7x+7(x+1)=189}$

==> $\mathsf{7[x+(x+1)]=189}$

==> $\mathsf{7(2x+1)=189}$

==> $\mathsf{2x+1=\frac{189}{7}}$

==> $\mathsf{2x+1=27}$

==> $\mathsf{2x=27-1=26}$

∴ $\mathsf{x=\frac{26}{2}=13}$

Hence the smaller multiple is $\mathsf{7x=7\times13=91}$.

$\textsf{\textbf{Verification:}}$

The other number is $\mathsf{7(x+1)=7(13+1)=7\times14=98}$.

$\mathsf{LHS = 7x + 7(x+1) = 91+98=189}\\\mathsf{RHS = 189}$

∴ $\mathsf{LHS = RHS, \: hence \: verified.}$

Answer: 91

I hope this helps. :D