Question 267345
In words:
(gallons of juice in 1st solution + gallons of juice in 2nd solution / (gallons of final solution) = 12%
Let {{{a}}} = gallons of 30% solution needed
Let {{{b}}} = gallons of 10% solution needed
given:
(1) {{{a + b = 100}}}
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{{{(.3a + .1b)/100 = .12}}}
{{{.3a + .1b = 12}}}
(2) {{{3a + b = 120}}}
Now subtract (1) from (2)
(2) {{{3a + b = 120}}}
(1) {{{-a - b = -100}}}
{{{2a = 20}}}
{{{a = 10}}}
and, since
{{{a + b = 100}}}
{{{b = 100 - 10}}}
{{{b = 90}}}
10 gallons of the 30% solution were needed
check:
{{{(.3a + .1b)/100 = .12}}}
{{{(.3*10 + .1*90)/100 = .12}}}
{{{(3 + 9)/100 = .12}}}
{{{12/100 = .12}}}
{{{.12 = .12}}}
OK