The ratio of A and B is 3:7 and the sum of the LCM and HCF of A and B is 352. Find A+B.

show your answer with complete and detailed steps. Do NOT use scientific notation. Use decimals or surd form if necessary. All surds must be simplified.

Supermomo May 28, 2020

#1**+2 **

**The ratio of A and B is 3:7 and the sum of the LCM and HCF of A and B is 352. Find A+B.**

\(\begin{array}{|rcll|} \hline \dfrac{A}{B} &=& \dfrac{3}{7} \\\\ \dfrac{A}{B} &=& \dfrac{3n}{7n} \\ \hline A &=& 3n \\ B &=& 7n \\ \mathbf{A+B} &=& \mathbf{10n} \\ \hline \end{array} \)

\(\begin{array}{|rcll|} \hline LCM(3n,\ 7n) &=& 3*7*n \\ \mathbf{LCM(3n,\ 7n)} &=& \mathbf{21n} \\ \mathbf{HCF(3n,\ 7n)} &=& \mathbf{n} \\ \hline LCM(3n,\ 7n)+ HCF(3n,\ 7n) &=& 21n+n \\ LCM(3n,\ 7n)+ HCF(3n,\ 7n) &=& 22n \quad | \quad LCM(3n,\ 7n)+ HCF(3n,\ 7n) = 352 \\ 352 &=& 22n \\ n &=& \dfrac{352}{22} \\ \mathbf{n} &=& \mathbf{16} \\ \hline \end{array} \)

\(\begin{array}{|rcll|} \hline \mathbf{A+B} &=& \mathbf{10n} \quad | \quad n=16 \\ A+B &=& 10*16 \\ \mathbf{A+B} &=& \mathbf{160} \\ \hline \end{array}\)

heureka May 28, 2020