Question 625725
Let {{{ a }}} = pounds of tin to be added
Let {{{ b }}} = pounds of lead to be added
{{{ .5*700 = 350 }}}  pounds of tin in original alloy
{{{ .25*700 = 175 }}} pounds of lead in original alloy
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given:
(1) {{{ ( a + 350 ) / ( a + b + 700 ) = .6 }}}
(2) {{{ ( b + 175 ) / ( a + b + 700 ) = .2 }}}
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(1) {{{ a + 350 = .6*( a + b + 700 ) }}}
(1) {{{ a + 350 = .6a + .6b + 420 }}}
(1) {{{ .4a - .6b = 420 - 350 }}}
(1) {{{ .4a - .6b = 70 }}}
(1)  {{{ 4a - 6b = 700 }}}
and
(2) {{{ ( b + 175 ) / ( a + b + 700 ) = .2 }}}
(2) {{{ b + 175 = .2*( a + b + 700 ) }}}
(2) {{{ b + 175 = .2a + .2b + 140 }}}
(2) {{{ .8b - .2a  = 140 - 175 }}}
(2) {{{ .8b - .2a = -35 }}}
(2) {{{ 2a - 8b = 350 }}}
Multiply both sides of (2) by {{{2}}}
and subtract (2) from (1)
(1)  {{{ 4a - 6b = 700 }}}
(2) {{{ -4a + 16b = -700 }}}
{{{ 10b = 0 }}}
{{{ b = 0 }}}
and, since
(2) {{{ 2a - 8b = 350 }}}
(2) {{{ 2a - 8*0 = 350 }}}
(2) {{{ 2a = 350 }}}
(2) {{{ a = 175 }}}
175 pounds of tin should be added and
no lead should be added
check answer:
(1) {{{ ( a + 350 ) / ( a + b + 700 ) = .6 }}}
(1) {{{ ( 175 + 350 ) / ( 175 + 0 + 700 ) = .6 }}}
(1) {{{ 525 / 875 = .6 }}}
(1) {{{ 21/35 = .6 }}}
(1) {{{ 21 = 21 }}}
OK
(2) {{{ ( b + 175 ) / ( a + b + 700 ) = .2 }}}
(2) {{{ ( 0 + 175 ) / ( 175 + 0 + 700 ) = .2 }}}
(2) {{{ 175 / 875 = .2 }}}
(2( {{{ 175 = 175 }}}
OK