Question 988546
Let {{{ a }}} = pounds of peanuts needed
Let {{{ b }}} = pounds of walnuts needed
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(1) {{{ a + b = 100 }}}
(2) {{{ ( 1.47a + 2.67b ) / 100 = 2.43 }}}
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(2) {{{ 1.47a + 2.67b = 243 }}}
(2) {{{ 147a + 267b = 24300 }}}
Multiply both sides of (1) by {{{ 147 }}} 
and subtract (1) from (2)
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(2) {{{ 147a + 267b = 24300 }}}
(1) {{{ -147a - 147b = -14700 }}}
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{{{ 120b = 9600 }}}
{{{ b = 80 }}}
and
(1) {{{ a + 80 = 100 }}}
(1) {{{ a = 20 }}}
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20 pounds of peanuts are needed
80 pounds of walnuts are needed
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check:
(2) {{{ ( 1.47a + 2.67b ) / 100 = 2.43 }}}
(2) {{{ ( 1.47*20 + 2.67*80 ) / 100 = 2.43 }}}
(2) {{{ ( 29.4 + 213.6 ) / 100 = 2.43 }}}
(2) {{{ 243/100 = 2.43 }}}
(2) {{{ 243 = 243 }}}
OK