Question 557001
Let {{{a}}} = pounds of peanuts needed
Let {{{b}}} = pounds of pecans needed
given:
(1) {{{ a + b = 30 }}} pounds
(2) {{{ ( 3.25a + 5.75b ) / 30 = 4.75 }}}
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(2) {{{ 3.25a + 5.75b = 4.75*30 }}}
(2) {{{ 3.25a + 5.75b = 142.5 }}}
(2) {{{ 325a + 575b = 14250 }}}
(2) {{{ 13a + 23b = 570 }}}
Multiply both sides of (1) by {{{ 13 }}}
and subtract (1) from (2)
(2) {{{ 13a + 23b = 570 }}}
(1) {{{ -13a - 13b = -390 }}}
{{{ 10b = 180 }}}
{{{ b = 18 }}}
and, since
(1) {{{ a + b = 30 }}}
(1) {{{ a + 18 = 30 }}}
(1) {{{ a = 12 }}}
12 pounds of peanuts are needed
18 pounds of pecans are needed
check answer:
(2) {{{ ( 3.25*12 + 5.75*18 ) / 30 = 4.75 }}}
(2) {{{ ( 39 + 103.5 ) / 30 = 4.75 }}}
(2) {{{ 142.5 / 30 = 4.75 }}}
(2) {{{ 142.5 = 142.5 }}}
OK