Question 899324
Let {{{ a }}}= pounds of v.c. needed
Let {{{ b }}} = pounds of i.c. needed
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(1) {{{ a + b = 12 }}}
(2) {{{ ( 18a + 30b ) / 12 = 25 }}}
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(2) {{{ 18a + 30b = 300 }}}
(2) {{{ 6a + 10b = 100 }}}
(2) {{{ 3a + 5b = 50 }}}
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Multiply both sides of (1) by {{{ 3 }}}
and subtract (1) from (2)
(2) {{{ 3a + 5b = 50 }}}
(1) {{{ -3a -3b = -36 }}}
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{{{ 2b = 14 }}}
{{{ b = 7 }}}
and, since
(1) {{{ a + b = 12 }}}
(1) {{{ a = 5 }}}
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5 pounds of v.c. are needed
7 pounds of i.c. are needed
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check:
(2) {{{ ( 18*5 + 30*7 ) / 12 = 25 }}}
(2) {{{ ( 90 + 210 ) / 12 = 25 }}}
(2) {{{ 300 / 12 = 25 }}}
(2) {{{ 300 = 300 }}}
OK