Question 178568
Let {{{a}}}= the pounds of the more expensive tea needed
Let {{{b}}}= the pounds of the less expensive tea needed
given:
(1) {{{a + b = 80}}}
(2) {{{345a + 215b = 80*275}}} (in cents)
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In words, (2) says 
(lbs of 'a' tea x price/lb) + (lbs of 'b' tea x price/lb) = 
(lbs of mixture x price/lb of mixture)
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Multiply both sides of (1) by {{{215}}} and then
subtract from (2)
{{{345a + 215b = 80*275}}} 
{{{-215a - 215b = -80*215}}}
{{{130a = 80*60}}}
{{{130a = 4800}}}
{{{a = 36.92}}}
and, from (1)
(1) {{{a + b = 80}}}
{{{36.92 + b = 80}}}
{{{b = 80 - 36.92}}}
{{{b = 43.08}}}
36.92 lbs of the $3.45 tea and 43.08 lbs of the $2.15 tea are needed
check answer:
(2) {{{345a + 215b = 80*275}}}
(2) {{{345*36.92 + 215*43.08 = 80*275}}}
{{{12740 + 9260 = 22000}}}
{{{22000 = 22000}}}
OK