Question 722190
Let {{{ c }}} = pounds of cashews needed
Let {{{ p }}} = pounds of peanuts needed
given:
(1) {{{ c + p = 25 }}}
(2) {{{ 5c + 2p = 92 }}}
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Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 5c + 2p = 92 }}}
(1) {{{ -2c - 2p = -50 }}}
{{{ 3c = 42 }}}
{{{ c = 14 }}}
and, since
(1) {{{ c + p = 25 }}}
(1) {{{ 14 + p = 25 }}}
(1) {{{ p = 11 }}}
14 pounds of cashews are needed
11 pounds of peanuts are needed
check:
(2) {{{ 5c + 2p = 92 }}}
(2) {{{ 5*14 + 2*11 = 92 }}}
(2) {{{ 70 + 22 = 92 }}}
(2) {{{ 92 = 92 }}}
OK