Question 544061
Let {{{ a }}} = pounds of the 10% cereal mix needed
Let {{{ b }}} = pounds of the 40% cereal mix needed
given:
{{{ .1a }}} = pounds of cereal in 10% cereal mix
{{{ .4b }}} = pounds of cereal in 40% cereal mix
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In words:
( total pounds of cereal in final mix ) / ( total pounds in final mix ) = 25%
(1) {{{ a + b = 40 }}}
(2) {{{ ( .1a + .4b ) / 40 = .25 }}}
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(2) {{{ .1a + .4b = .25*40 }}}
(2) {{{ .1a + .4b = 10 }}}
(2) {{{ a + 4b = 100 }}}
Subtract (1) from (2)
(2) {{{ a + 4b = 100 }}}
(1) {{{ -a - b = -40 }}}
{{{ 3b = 60 }}}
{{{ b = 20 }}}
and, since
(1) {{{ a + b = 40 }}}
(1) {{{ a + 20 = 40 }}}
(1) {{{ a = 20 }}}
20 pounds of the 10% cereal mix is needed
check answer:
(2) {{{ ( .1a + .4b ) / 40 = .25 }}}
(2) {{{ ( .1*20 + .4*20 ) / 40 = .25 }}}
(2) {{{ ( 2 + 8 ) / 40 = .25 }}}
(2) {{{ 10/40 = .25 }}}
(2) {{{ 10 = 10 }}}
OK