Respuesta :
we know that solution A is 40% of acid, so let's say that there are "x" liters in solution A, that means that only 40% of A is acid, or namely (40/100) * x = 0.4x.
likewise we can say the same about solution B that is 70% of acid, if there are "y" liters of solution total, the amount of acide in it wil be (70/100) * y = 0.7y
[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{liters of }}{amount}\\ \cline{2-4}&\\ A&x&0.4&0.4x\\ B&y&0.7&0.7y\\ \cline{2-4}&\\ mixture&100&0.61&61 \end{array}~\hfill \implies ~\hfill \begin{cases} x+y = 100\\\\ 0.4x+0.7y = 61 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=100\implies y = 100-x} \\\\\\ \stackrel{\textit{substituting in the 2nd equation}}{0.4x+0.7(100-x)=61}\implies 0.4x+70-0.7x = 61 \\\\\\ 70-0.3x=61\implies -0.3x=-9\implies x = \cfrac{-9}{-0.3}\implies \boxed{x = 30} \\\\\\ \stackrel{\textit{we know that}}{y = 100 -x}\implies y = 100 - 30\implies \boxed{y = 70}[/tex]
