Question 815060
2% is {{{ 2/100 = .02 }}}
4% is {{{ 4/100 = .04 }}}
Plain coal tar is 100% = {{{ 100/100 = 1 }}}
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Let {{{ a}}} = units of 2% coal tar needed
Let {{{ b }}} = units of 100% coal tar needed
( I will choose units for {{{a}}} and {{{b}}} 
so that {{{a + b = 10 }}} units
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(1) {{{ ( .02a + 1*b ) / ( a + b ) = .04 }}}
(2) {{{ a + b = 10 }}}
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(1) {{{ .02a + b = .04*( a + b ) }}}
(1) {{{ .02a + b = .04a + .04b ) }}}
(1) {{{ .96b - .02a = 0 }}}
and
(2) {{{ a = 10 - b }}}
by substitution:
(1) {{{ .96b -.02*( 10 - b ) = 0 ) }}}
(1) {{{ .96b - .2 + .02b = 0 }}}
(1) {{{ .98b = .2 }}}
(1) {{{ b = 10/49 }}}
and, since
(2) {{{ a = 10 - b }}}
(2) {{{ a = 10 - 10/49 }}}
(2) {{{ a = 490/49 - 10/49 }}}
(2) {{{ a = 480/49 }}}
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The proportion of plain coal tar to 2% coal tar
should be:
{{{ b/a = ( 1/49 ) / ( 480/49 ) }}}
{{{ b/a = 1/480  }}}
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check answer:
(1) {{{ ( .02a + 1*b ) / 10 = .04 }}}
(1) {{{  .02a + b  = .4 }}}
(1) {{{ .02a = .4 - b }}}
(1) {{{ .02*( 480/49 ) = .4 - 10/49 }}}
Multiply both sides by {{{ 49 }}}
(1) {{{ .02*480 = .4*49 - 10 }}}
(1) {{{ 9.6 = 19.6 - 10 }}}
(1) {{{ 9.6 = 9.6 }}}
OK