Question 972705
Let {{{ a }}} = pounds of peanuts needed
Let {{{ b }}} = pounds of walnuts needed
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(1) {{{ ( .9a + 1.6b ) / 175 = 1.3 }}}
(2) {{{ a + b = 175 }}}
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(1) {{{ .9a + 1.6b = 1.3*175 }}}
(1) {{{ .9a + 1.6b = 227.5 }}}
(1) {{{ 9a + 16b = 2275 }}}
Multiply both sides of (2) by {{{ 9 }}}
and subtract (2) from (1)
(1) {{{ 9a + 16b = 2275 }}}
(2) {{{ -9a - 9b = -1575 }}}
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{{{ 7b = 700 }}}
{{{ b = 100 }}}
and
(2) {{{ a + 100 = 175 }}}
(2) {{{ a = 75 }}}
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75 pounds of peanuts and 100 pounds 
of walnuts are needed
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check:
(1) {{{ ( .9a + 1.6b ) / 175 = 1.3 }}}
(1) {{{ ( .9*75 + 1.6*100 ) / 175 = 1.3 }}}
(1) {{{ ( 67.5 + 160 ) / 175 = 1.3 }}}
(1) {{{ 227.5 / 175 = 1.3 }}}
(1) {{{ 227.5 = 227.5 }}}
OK