Question 910903
Let {{{ a }}} = pounds of peanuts needed
Let {{{ b }}} = pounds of trail mix needed
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(1) {{{ a + b = 10 }}}
(2) {{{ ( 2a + 5b ) / 10 = 3.2 }}}
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(2) {{{ 2a + 5b = 32 }}}
Multiply both sides of (1) by {{{ 2 }}} and
subtract (1) from (2)
(2) {{{ 2a + 5b = 32 }}}
(1) {{{ -2a - 2b = -20 }}}
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{{{ 3b = 12 }}}
{{{ b = 4 }}}
and, since
(1) {{{ a + b = 10 }}}
(1) {{{ a + 4 = 10 }}}
(1) {{{ a = 6 }}}
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6 pounds of peanuts and
4 pounds of trail mix are needed
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check:
(2) {{{ ( 2*6 + 5*4 ) / 10 = 3.2 }}}
(2) {{{ ( 12 + 20 ) / 10 = 3.2 }}}
(2) {{{ 32 = 32 }}}
OK