Question 1014807
Let {{{ a }}} = pounds of Earl Grey needed
Let {{{ b }}} = pounds of Orange Pekoe needed
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(1) {{{ a + b = 100 }}}
(2) {{{ ( 5a + 3b ) / 100 = 4.5 }}}
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Multiply both sides of (1) by {{{ 3 }}}
and subtract (1) from (2)
(2) {{{ 5a + 3b = 450 }}}
(1) {{{ -3a - 3b = -300 }}}
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{{{ 2a = 150 }}}
{{{ a = 75 }}}
and
(1) {{{ a + b = 100 }}}
(1) {{{ b = 25 }}}
75 pounds of Earl Grey are needed
25 pounds of Orange Pekoe are needed
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check:
(2) {{{ ( 5a + 3b ) / 100 = 4.5 }}}
(2) {{{ ( 5*75 + 3*25 ) / 100 = 4.5 }}}
(2) {{{ ( 375 + 75 ) / 100 = 4.5 }}}
(2) {{{ 450 = 450 }}}
OK