Question 886399
Let {{{ a }}} = kilos of 1st class sugar needed
Let {{{ b }}} = kilos of 3rd class sugar needed
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Given:
(1) {{{ a + b = 50 }}}
(2) {{{ ( 3.5a + 2b ) / 50 = 2.9 }}}
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(2) {{{ 3.5a + 2b = 2.9*50 }}}
(2) {{{ 3.5a + 2b = 145 }}}
(2) {{{ 35a + 20b = 1450 }}}
Multiply both sides of (1) by {{{ 20 }}}
and subtract (1) from (2)
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(2) {{{ 35a + 20b = 1450 }}}
(1) {{{ -20a - 20b = -1000 }}}
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{{{ 15a = 450 }}}
{{{ a = 30 }}}
and
(1) {{{ 30 + b = 50 }}}
(1) {{{ b = 20 }}}
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30 kilos of 1st class sugar are needed
20 kilos of 3rd class sugar are needed
check answer:
(2) {{{ ( 3.5a + 2b ) / 50 = 2.9 }}}
(2) {{{ ( 3.5*30 + 2*20 ) / 50 = 2.9 }}}
(2) {{{ ( 105 + 40 ) / 50 = 2.9 }}}
(2) {{{ 145 = 2.9*50 }}}
(2) {{{ 145 = 145 }}}
OK