Question 125825
Let {{{a}}} = the amount of 4.5% mixture needed
Let {{{b}}} = the amount of 9.75% mixture needed
In words:
(alcohol in the two mixtures) / (total mixture) = 7.25%
{{{(.045a + .0975b) / (a + b) = .0725}}}
also given is
{{{a + b = 300}}}
{{{b = 300 - a}}}
{{{(.045a + .0975(300 - a)) / 300 = .0725}}}
{{{(.045a + 29.25 - .0975a) / 300 = .0725}}}
{{{ .045a + 29.25 - .0975a = 21.75}}}
{{{-.0525a = -7.5}}}
{{{a = 142.857}}} liters answer
{{{b = 300 - 142.857}}}
{{{b = 157.143}}} liters answer
check:
{{{(.045a + .0975b) / (a + b) = .0725}}}
{{{(.045*142.857 + .0975*157.143) / 300 = .0725}}}
{{{(6.429 + 15.321) / 300 = .0725}}}
{{{21.75 / 300 = .0725}}}
{{{21.75 = 21.75}}}
OK