Question 779027
Let {{{ a }}} = pounds of almonds needed
Let {{{ b }}} = pounds of peanuts needed
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(1) {{{ ( 6.5a + 4b ) / 50 = 5  }}}
(2) {{{ a + b = 50 }}}
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(1) {{{ 6.5a + 4b = 250 }}}
(1) {{{ 65a + 40b = 2500 }}}
Multiply both sides of (2) by {{{ 40 }}}
and subtract (2) from (1)
(1) {{{ 65a + 40b = 2500 }}}
(2) {{{ -40a - 40b = -2000 }}}
{{{ 25a = 500 }}}
{{{ a = 20 }}}
and, since
(2) {{{ a + b = 50 }}}
(2) {{{ b = 30 }}}
The owner needs 20 pounds of almonds and
30 pounds of peanuts
check:
(1) {{{ ( 6.5*20 + 4*30 ) / 50 = 5  }}}
(1) {{{ ( 130 + 120 ) / 50 = 5 }}}
(1) {{{ 250 = 250 }}}
OK