Question 560317
Let {{{ a }}} = pounds of H.P.S. needed
Let {{{ b }}} = pounds of V.S needed
given:
{{{ 6.75a }}} = cost of H.P.S. in mixture
{{{ 3.25b }}} = cost of V.S. in mixture
(1) {{{ a + b = 5 }}}
(2) {{{ ( 6.75a + 3.25b ) / 5 = 4.65 }}}
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(2) {{{ 6.75a + 3.25b = 23.25 }}}
(2) {{{ 675a + 325b = 2325 }}}
divide both sides by {{{ 25 }}}
(2) {{{ 27a + 13b = 93 }}}
Multiply both sides of (1) by {{{ 13 }}}
and subtract (1) from (2)
(2) {{{ 27a + 13b = 93 }}}
(1) {{{ -13a - 13b = -65 }}}
{{{ 14a = 28 }}}
{{{ a = 2 }}}
and since
(1) {{{ a + b = 5 }}}
(1) {{{ 2 + b = 5 }}}
(1) {{{ b = 3 }}}
2 pounds of H.P.S.are needed
3 pounds of V.S are needed
check answer:
(2) {{{ ( 6.75a + 3.25b ) / 5 = 4.65 }}}
(2) {{{ ( 6.75*2 + 3.25*3 ) / 5 = 4.65 }}}
(2) {{{ (13.5 + 9.75 ) / 5 = 4.65 }}}
(2) {{{ 23.25 = 5*4.65 }}}
(2) {{{ 23.25 = 23.25 }}}
OK