+0

# Ratio 2

-1
91
1
+3

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.

May 28, 2020
edited by Supermomo  May 28, 2020

#1
+25541
+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.

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

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

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

May 28, 2020