Question 758555
Let {{{ a }}} = pounds of 38 cents/pound feed needed
Let {{{ b }}} = pounds of 56 cents/pound feed needed
{{{ 38a }}} = cost of 38 cents/pound feed used
{{{ 56b }}} = cost of 56 cents/pound feed used
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(1) {{{ a + b = 24 }}}
(2) {{{ ( 38a + 56b ) / 24 = 49 }}}
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(2) {{{ 38a + 56b = 24*49 }}}
(2) {{{ 38a + 56b = 1176 }}}
Multiply both sides of (1) by {{{ 38 }}}
and subtract (1) from (2)
(2) {{{ 38a + 56b = 1176 }}}
(1) {{{ -38a - 38b = -912 }}}
{{{ 18b = 264 }}}
{{{ b = 14.667 }}}
and, since
(1) {{{ a + b = 24 }}}
(1) {{{ a + 14.667 = 24 }}}
(1) {{{ a = 9.333 }}}
9.333 pounds of 38 cents/pound feed is needed
check:
(2) {{{ ( 38a + 56b ) / 24 = 49 }}}
(2) {{{ ( 38*9.333 + 56*14.667 ) / 24 = 49 }}}
(2) {{{ 354.654 + 821.352 = 24*49 }}}
(2) {{{ 354.654 + 821.352 = 1176 }}}
(2) {{{ 1176.006 = 1176 }}}
close enough