Question 138707
Let {{{a}}} = the kgs of $.80/kg cookies needed
Let {{{b}}} = the kgs of $.95/kg cookies needed
In words, the problem is:
(kgs $.80/kg cookies) x ($.80/kg) + (kgs $.95/kg cookies) x ($.95/kg) /
(kgs $.80/kg cookies + kgs $.95/kg cookies) = $.85/kg
or in symbols,
{{{(.8a + .95b) / (a + b) = .85}}} cents/kg
Also given is:
{{{a + b = 60}}} kg
{{{(.8a + .95b) / 60 = .85}}}
{{{.8a + .95b = 60*.85}}}
{{{.8a + .95(60 - a) = 51}}}
{{{.8a + 57 - .95a = 51}}}
{{{-.15a = -6}}}
{{{a = 40}}}
{{{b = 60 - a}}}
{{{b = 60 - 40}}}
{{{b = 20}}}
The grocer needs to mix 40 kg of $.80/kg cookies and 20 kg of $.95/kg
cookies
check answer:
{{{(.8a + .95b) / (a + b) = .85}}}
{{{(.8*40 + .95*20) / 60 = .85}}}
{{{(32 + 19)/ 60 = .85}}}
{{{51/60 = .85}}}
{{{.85 = .85}}}
OK