Question 1013750
Let {{{ a }}} = pounds of Earl Gray needed
Let {{{ b }}} = pounds of Orange Pekoe needed
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(1) {{{ a + b = 900 }}}
(2) {{{ ( 4a + 2b ) / 900 = 2.5 }}}
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(2) {{{ 4a + 2b = 2.5*900 }}}
(2) {{{ 4a + 2b = 2250 }}}
(2) {{{ 2a + b = 1125 }}}
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Subtract (1) from (2)
(2) {{{ 2a + b = 1125 }}}
(1) {{{ -a - b = -900 }}}
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{{{ a = 225 }}}
and
(1) {{{ a + b = 900 }}}
(1) {{{ 225 + b = 900 }}}
(1) {{{ b = 675 }}}
225 pounds of Earl Gray are needed
675 pounds of Orange Pekoe are needed
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check:
(2) {{{ ( 4a + 2b ) / 900 = 2.5 }}}
(2) {{{ ( 4*225 + 2*675 ) / 900 = 2.5 }}}
(2) {{{ ( 900 + 1350 ) / 900 = 2.5 }}}
(2) {{{ 2250 = 2.5*900 }}}
(2) {{{ 2250 = 2250 }}}
OK