Question 754396
Let {{{ h }}} = pounds of hazelnuts needed
Let {{{ c }}} = pounds of cashews needed
{{{ 6.5h }}} = cost of hazlenuts
{{{ 4.5c }}} = cost of cashews
{{{ 5.1*60 = 306 }}} = cost of mixture
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(1) {{{ h + c = 60 }}}
(2) {{{ 6.5h + 4.5c = 306 }}}
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(2) {{{ 65h + 45c = 3060 }}}
(2) {{{ 13h + 9c = 612 }}}
Multiply both sides of (1) by {{{ 9 }}}
and subtract (1) from (2)
(2) {{{ 13h + 9c = 612 }}}
(1) {{{ -9h - 9c = -540 }}}
{{{ 4h = 72 }}}
{{{ h = 18 }}}
and, since
(1) {{{ h + c = 60 }}}
(1) {{{ c = 60 - 18 }}}
(1) {{{ c = 42 }}}
18 pounds of hazelnuts are needed
42 pounds of cashews are needed
check:
(2) {{{ 6.5h + 4.5c = 306 }}}
(2) {{{ 6.5*18 + 4.5*42 = 306 }}}
(2) {{{ 117 + 189 = 306 }}}
(2) {{{ 306 = 306 }}}