Question 485684
Let {{{ n }}} = pounds of nuts to be used
Let {{{ c }}} = pounds of cashews to be used
given:
(1) {{{ n + c = 125 }}}
(2) {{{ 2.65n + 4.9c = 3.28*125 }}}
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Multiply both sides of (2) by {{{ 100 }}}
(2) {{{ 265n + 490c = 41000 }}}
Multiply both sides of (1) by {{{ 265 }}} and
subtract (1) from (2)
(2) {{{ 265n + 490c = 41000 }}}
(1) {{{ -265n - 265c = -33125 }}}
{{{ 225c = 7875 }}}
{{{ c = 35 }}}
and, since
(1) {{{ n + c = 125 }}}
(1) {{{ n + 35 = 125 }}}
(1) {{{ n = 90 }}}
90 pounds of nuts are to be used
35 pounds of cashews are to be used
check:
(2) {{{ 2.65n + 4.9c = 3.28*125 }}}
(2) {{{ 2.65*90 + 4.9*35 = 3.28*125 }}}
(2) {{{ 238.5 + 171.5 = 410 }}}
(2) {{{ 410 = 410 }}}