Question 722370
Let {{{ a }}} = tons of 80% crushed rock needed
Let {{{ b }}} = tons of 30% crushed rock needed
given:
(1) {{{ a + b = 150 }}}
(2) {{{ ( .8a + .3b ) / 150 = .4 }}}
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(2) {{{ .8a + .3b = .4*150 }}}
(2) {{{ .8a + .3b = 60 }}}
(2) {{{ 8a + 3b = 600 }}}
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Multiply both sides of (1) by {{{3}}}
and subtract (1) from (2)
(2) {{{ 8a + 3b = 600 }}}
(1) {{{ -3a - 3b = -450 }}}
{{{ 5a = 150 }}}
{{{ a = 30 }}}
and, since
(1) {{{ a + b = 150 }}}
(1) {{{ 30 + b = 150 }}}
(1) {{{ b = 120 }}}
30 tons of 80% crushed rock are needed
120 tons of 30% crushed rock are needed
check:
(2) {{{ ( .8a + .3b ) / 150 = .4 }}}
(2) {{{ ( .8*30 + .3*120 ) / 150 = .4 }}}
(2) {{{ ( 24 + 36 ) / 150 = .4 }}}
(2) {{{ 60 = .4*150 }}}
(2) {{{ 60 = 60 }}}
OK