Question 1066871
Here's the way I solve this type of problem:
Let {{{ a }}} = pounds of pecans in mixture
Let {{{ b }}} = pounds of cashews in mixture
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(1) {{{ a + b = 100 }}}
(2) {{{ ( 1.12a + .6b ) / 100 = .73 }}}
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You did the same thing so far
(2) {{{ 1.12a + .6b = 73 }}}
Multiply both sides by {{{ 100 }}}
(2) {{{ 112a + 60b = 7300 }}}
Divide both sides by {{{ 4 }}}
(2) {{{ 28a + 15b = 1825 }}}
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Multiply both sides of (1) by {{{ 15 }}}
and subtract (1) from (2)
(2) {{{ 28a + 15b = 1825 }}}
(1) {{{ -15a - 15b = -1500 }}}
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{{{ 13a = 325 }}}
{{{ a = 25 }}}
and
(1) {{{ a + b = 100 }}}
(1) {{{ 25 + b = 100 }}}
(1) {{{ b = 75 }}}
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25 pounds of pecans in the mixture
75 pounds of cashews in the mixture
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check:
(2) {{{ ( 1.12a + .6b ) / 100 = .73 }}}
(2) {{{ ( 1.12*25 + .6*75 ) / 100 = .73 }}}
(2) {{{ ( 28 + 45 ) / 100 = .73 }}}
(2) {{{ 73/100 = .73 }}}
OK
Sorry I did the whole thing -got carried away