Question 739702
Let {{{ a }}} = kg of 50% fat chocolate needed
Let {{{ b }}} = kg of 30% fat chocolate needed
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(1) {{{ a + b = 20 }}} kg
(2) {{{ ( .5a + .3b ) / 20 = .45 }}}
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(2) {{{ .5a + .3b = .45*20 }}}
(2) {{{ .5a + .3b = 9 }}}
(2) {{{ 5a + 3b = 90 }}}
Multiply both sides of (1) by {{{ 3 }}}
and subtract (1) from (2)
(2) {{{ 5a + 3b = 90 }}}
(1) {{{ -3a - 3b = -60 }}}
{{{ 2a = 30 }}}
{{{ a = 15 }}}
and, since
(1) {{{ a + b = 20 }}}
(1) {{{ b = 5 }}}
15 kg of 50% fat chocolate are needed
5 kg of 30% fat chocolate are needed
check:
(2) {{{ ( .5a + .3b ) / 20 = .45 }}}
(2) {{{ ( .5*15 + .3*5 ) / 20 = .45 }}}
You can check