Question 596032
Let {{{ p }}} = kg of pecans
Let {{{ c }}} = kg of cashews
Cost of pecans used = {{{ 9p }}}
Cost of cashews used = {{{ 8c }}}
Cost of mixture = {{{ 8.4*10 = 84 }}}
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(1) {{{ 9p + 8c = 84 }}}
(2) {{{ p + c = 10 }}}
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Multiply both sides of (2) by {{{ 8 }}}
and subtract (2) from (1)
(1) {{{ 9p + 8c = 84 }}}
(2) {{{ -8p - 8c = -80 }}}
{{{ p = 4 }}}
and, since
(2) {{{ p + c = 10 }}}
(2) {{{ 4 + c = 10 }}}
(2) {{{ c = 6 }}} 
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There are 4 kg of pecans in the mixture
check answer:
(1) {{{ 9p + 8c = 84 }}}
(1) {{{ 9*4 + 8*6 = 84 }}}
(1) {{{ 36 + 48 = 84 }}}
(1) {{{ 84 = 84 }}}
OK