Respuesta :
x = amount of the 60% solution
y = amount of the 75% solution
now, how much is 60% of x? well, (60/100) * x, or 0.6x.
and how much is 75% of y? well, (75/100) * y, or 0.75y.
well, the resulting mixture is 72% of acid and then water or other liquids, but we know is that much off 20 liters, how much is that then? well 72% of 20 is (72/100) * 20, or 14.4.
regardless of what "x" and "y" are, we know that the resulting substance has to be 20 liters, thus x + y = 20.
and we also know that the amount of acid in each amount, will add up to the acid in the resulting amount.
since we know that there is 0.6x liters of only acid and 0.75y liters of only acid in each, thus 0.6x + 0.75y = 14.4.
[tex]\bf \begin{array}{lccc} &\stackrel{liters}{amount}&\stackrel{\%~of~acid}{amount}&\stackrel{acid~liters}{quantity}\\ &------&------&------\\ \textit{60\% solution}&x&0.60&0.6x\\ \textit{75\% solution}&y&0.75&0.75y\\ ------&------&------&------\\ mixture&20&0.72&14.4 \end{array} \\\\\\ \begin{cases} x+y=20\implies \boxed{y}=20-x\\ 0.6x+0.75y=14.4\\ -------------\\ 0.6x+0.75\left( \boxed{20-x} \right)=14.4 \end{cases} \\\\\\ 0.6x-0.75x+15=14.4\implies -0.15x=-0.6 \\\\\\ x=\cfrac{-0.6}{-0.15}\implies x=4[/tex]
how many liters of "y"? well, y = 20 - x.
y = amount of the 75% solution
now, how much is 60% of x? well, (60/100) * x, or 0.6x.
and how much is 75% of y? well, (75/100) * y, or 0.75y.
well, the resulting mixture is 72% of acid and then water or other liquids, but we know is that much off 20 liters, how much is that then? well 72% of 20 is (72/100) * 20, or 14.4.
regardless of what "x" and "y" are, we know that the resulting substance has to be 20 liters, thus x + y = 20.
and we also know that the amount of acid in each amount, will add up to the acid in the resulting amount.
since we know that there is 0.6x liters of only acid and 0.75y liters of only acid in each, thus 0.6x + 0.75y = 14.4.
[tex]\bf \begin{array}{lccc} &\stackrel{liters}{amount}&\stackrel{\%~of~acid}{amount}&\stackrel{acid~liters}{quantity}\\ &------&------&------\\ \textit{60\% solution}&x&0.60&0.6x\\ \textit{75\% solution}&y&0.75&0.75y\\ ------&------&------&------\\ mixture&20&0.72&14.4 \end{array} \\\\\\ \begin{cases} x+y=20\implies \boxed{y}=20-x\\ 0.6x+0.75y=14.4\\ -------------\\ 0.6x+0.75\left( \boxed{20-x} \right)=14.4 \end{cases} \\\\\\ 0.6x-0.75x+15=14.4\implies -0.15x=-0.6 \\\\\\ x=\cfrac{-0.6}{-0.15}\implies x=4[/tex]
how many liters of "y"? well, y = 20 - x.
