Question 697694
Let {{{ a }}} = pounds of almonds needed
Let {{{ b }}} = pounds of walnuts needed
Let {{{ c }}} = pounds of peanuts needed
given:
(1) {{{ a + b + c = 21 }}}
(2) {{{ ( 1.8a + 1.3b + .65c ) / 21 = 1 }}} ( the {{{ 1 }}} is $1/pound )
(3) {{{ c = 2b }}}
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This is 3 equations with 3 unknowns, so it's solvable
(2) {{{ 1.8a + 1.3b + .65c = 21 }}}
(2) {{{ 180a + 130b + 65c = 2100 }}}
(2) {{{ 36a + 26b + 13c = 420 }}}
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Multiply both sides of (1) by {{{ 13 }}}
and subtract (1) from (2)
(2) {{{ 36a + 26b + 13c = 420 }}}
(1) {{{ -13a - 13b - 13c = -273 }}}
{{{ 23a + 13b = 147 }}}
{{{ 23a = 147 - 13b }}}
{{{ a = ( 147 - 13b ) / 23 }}}
Substitute this result and (3) into (1)
(1) {{{ a + b + c = 21 }}}
(1) {{{ ( 147 - 13b ) / 23 + b + 2b = 21 }}}
(1) {{{ 147 - 13b + 23b + 46b = 483 }}}
(1) {{{ 56b = 483 - 147 }}}
(1) {{{ 56b = 336 }}}
(1) {{{ b = 6 }}}
and, since
(3) {{{ c = 2b }}}
(3) {{{ c = 2*6 }}}
(3) {{{ c = 12 }}}
and
(1) {{{ a + b + c = 21 }}}
(1) {{{ a + 6 + 12 = 21 }}}
(1) {{{ a = 21 - 18 }}}
(1) {{{ a = 3 }}}
3 pounds of almonds are needed
6 pounds of walnuts are needed
12 pounds of peanuts are needed
check answer:
(2) {{{ ( 1.8a + 1.3b + .65c ) / 21 = 1 }}} 
(2) {{{ ( 1.8*3 + 1.3*6 + .65*12 ) / 21 = 1 }}} 
(2) {{{ 5.4 + 7.8 + 7.8 = 21 }}}
(2) {{{ 21 = 21 }}}
OK