Question 305402
She ends up with {{{.2*48 = 9.6}}} liters of acid in
48 liters of solution
Let {{{a}}} = liters of 15% solution to use
Let {{{b}}} = liters of 45% solution to use
(1) {{{(.15a + .45b)/48 = .2}}}
(1) {{{.15a + .45b = 9.6}}}
(1) {{{15a + 45b = 960}}}
and
(2) {{{a + b = 48}}}
Multiply both sides of (2) by {{{15}}} and
subtract (2) from (1)
---------------------
(1) {{{15a + 45b = 960}}}
(2) {{{-15a - 15b = -720}}}
{{{30b = 240}}}
{{{b = 8}}}
and
{{{a + 8 = 48}}}
{{{a = 40}}}
She must mix 40 liters of the 15% solution
with 8 liters of the 45% solution
check answer:
(1) {{{(.15a + .45b)/48 = .2}}}
(1) {{{(.15*40 + .45*8)/48 = .2}}}
{{{(6 + 3.6)/48 = .2}}}
{{{9.6/48 = .2}}}
{{{9.6 = 9.6}}}
OK