Question

How do you answer this following equation “ the sum of two numbers is 33 , and the sum of 7 times the first number and 5 times the second number is 197. What are the two numbers ? “

Answer 1

$\bf \begin{cases} a\\\\ b \end{cases}\qquad \qquad \begin{array}{llll} \stackrel{\textit{the sum of \underline{a} and \underline{b}}}{a+b=33}\\\\ \stackrel{\textit{the sum of 7 times \underline{a} and 5 times \underline{b}}}{7a+5b=197} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ a+b=33\implies \boxed{b}=33-a \\\\\\ \stackrel{\textit{substituting \boxed{b} in the second equation}}{7a+5\left(\boxed{33-a} \right)=197}\implies 7a+165-5a=197$

$\bf 2a+165=197\implies 2a=32\implies a=\cfrac{32}{2}\implies \blacktriangleright a=16 \blacktriangleleft \\\\\\ \boxed{b}=33-a\implies b=33-16\implies \blacktriangleright 17\blacktriangleleft$