Question 717257
Let {{{ a }}} = pounds of $7/lb tea needed
Let {{{ b }}} = pounds of $9/lb tea needed
{{{ 7a }}} = cost of $7/lb tea used
{{{ 9b }}} = cost of $9/lb tea used
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(1) {{{ a + b = 32 }}}
(2) {{{ ( 7a + 9b ) / 32 = 8.5 }}}
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(2) {{{ 7a + 9b = 8.5*32 }}}
(2) {{{ 7a + 9b = 272 }}}
Multiply both sides of (1) by {{{ 7 }}}
and subtract (1) from (2)
(2) {{{ 7a + 9b = 272 }}}
(1) {{{ -7a - 7b = -224 }}}
{{{ 2b = 48 }}}
{{{ b = 24 }}}
and, since
(1) {{{ a + 24 = 32 }}}
(1) {{{ a = 8 }}}
8 pounds of $7/lb tea are needed
24 pounds of $9/lb tea are needed
check answer:
(2) {{{ ( 7*8 + 9*24 ) / 32 = 8.5 }}}
(2) {{{ ( 56 + 216 ) / 32 = 8.5 }}}
(2) {{{ 272 / 32 = 8.5 }}}
(2) {{{ 272 = 272 }}}
OK