Question 679337
Let {{{ a }}} = pounds of $.29 / lb feed needed
Let {{{ b }}} = pounds of $.46 / lb feed needed
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given:
(1) {{{ a + b = 29 }}}
(2) {{{ ( .29a + .46b ) / 29 = .37 }}}
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(2) {{{ .29a + .46b = .37*29 }}}
(2) {{{ .29a + .46b = 10.73 }}}
(2) {{{ 29a + 46b = 1073 }}}
Multiply both sides of (1) by {{{ 29 }}}
and subtract (1) from (2)
(2) {{{ 29a + 46b = 1073 }}}
(1) {{{ -29a - 29b = -841 }}}
{{{ 17b = 232 }}}
{{{ b = 13.65 }}}
and, since
(1) {{{ a + 13.65 = 29 }}}
(1) {{{ a = 15.35 }}}
They should use 15.35 pounds of the cheaper feed
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check answer:
(2) {{{ ( .29a + .46b ) / 29 = .37 }}}
(2) {{{ ( .29*15.35 + .46*13.65 ) / 29 = .37 }}}
(2) {{{ ( 4.45 + 6.28 ) / 29 = .37 }}}
(2) {{{ 10.73 / 29 = .37 }}}
(2) {{{ 10.73 = .37*29 }}}
(2) {{{ 10.73 = 10.73 }}}
OK