Question 271155
In words:
(cost of Brand A in mix) + (cost of brand B in mix) = cost of mix
which is the same as:
(pounds of Brand A in mix) x (cost per pound) + (pounds of brand B in mix) x (cost per pound) = pounds of mix) x (cost per pound of mix)
Let {{{A}}} = pounds of brand A in mix
Let {{{B}}} = pounds of brand B in mix
(1) {{{A + B = 25}}}
{{{A*10.5 + B*5.75 = 25*8.22}}}
Multiply both sides by {{{100}}}
(2) {{{1050A + 575B = 20550}}}
and, from (1),
(1) {{{B = 25 - A}}}
By substitution:
(2) {{{1050A + 575*(25- A) = 20550}}}
{{{1050A + 14375 - 575A = 20550}}}
{{{475A = 6175}}}
{{{A = 13}}}
and, since
{{{B = 25 - A}}}
{{{B = 25 - 13}}}
{{{B = 12}}}
He needs 13 pounds of brand A and 12 pounds of brand B
check:
{{{A*10.5 + B*5.75 = 25*8.22}}}
{{{13*10.5 + 12*5.75 = 25*8.22}}}
{{{136.5 + 69 = 205.5}}}
{{{205.5 = 205.5}}}
OK