Question 708400
Let {{{ a }}} = pounds of candy at $6 per pound needed
Let {{{ b }}} = pounds of candy at $8 per pound needed
given:
(1) {{{  6a + 8b = 10*7.5 }}}
(2) {{{ a + b = 10 }}}
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(1) {{{ 6a + 8b = 75 }}}
Multiply both sides of (2) by {{{ 6 }}}
and subtract (2) from (1)
(1) {{{ 6a + 8b = 75 }}}
(2) {{{ -6a - 6b = -60 }}}
{{{ 2b = 15 }}}
{{{ b = 7.5 }}}
and, since
(2) {{{ a + b = 10 }}}
(2) {{{ a = 2.5 }}}
2.5 pounds of candy at $6/pound are needed
7.5 pounds of candy at $8/pound are needed
check:
(1) {{{ 6*2.5 + 8*7.5 = 75 }}}
(1) {{{ 15 + 60 = 75 }}}
(1) {{{ 75 = 75 }}}
OK