Question 502773
Let {{{a}}} = pounds of peanuts needed
Let {{{b}}} = pounds of cashews needed
Let {{{c}}} = pounds of Brazil nuts needed
given:
(1) {{{ a + b + c = 50 }}}
(2) {{{ ( 2a + 9b + 7c ) / 50 = 5.2 }}}
(3) {{{ b = a - 15 }}}
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(2) {{{ 2a + 9b + 7c = 260 }}}
Multiply both sides of (1) by {{{7}}} and
subtract (2) from (1)
(1) {{{ 7a + 7b + 7c = 350 }}}
(2) {{{ -2a - 9b - 7c = -260 }}}
{{{ 5a - 2b = 90 }}}
Substitute (3) into this result
{{{ 5a -2*( a - 15 ) = 90 }}}
{{{ 5a - 2a + 30 = 90 }}}
{{{ 3a = 60 }}}
{{{ a = 20 }}}
and, since
(3) {{{ b = a - 15 }}}
(3) {{{ b = 20 - 15 }}}
(3) {{{ b = 5 }}}
and, since
(1) {{{ a + b + c = 50 }}}
(1) {{{ 20 + 5 + c = 50 }}}
(1) {{{ c = 50 - 25 }}}
(1) {{{ c = 25 }}}
20 pounds of peanuts are needed
5 pounds of cashews are needed
25 pounds of Brazil nuts are needed
check answer:
(2) {{{ ( 2a + 9b + 7c ) / 50 = 5.2 }}}
(2) {{{ ( 2*20 + 9*5 + 7*25 ) / 50 = 5.2 }}}
(2) {{{ ( 40 + 45 + 175 ) / 50 = 5,2 }}}
(2) {{{ 260/50 = 5.2 }}}
(2) {{{ 260 = 260 }}}
OK