Question 915407
There is just lots of words -some of them not needed
Let {{{ a }}} = pounds of macadamias needed
Let {{{ b }}} = pounds of standard mix needed
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(1) {{{ a + b = 40 }}}
(2) {{{ ( 16.5a + 9.25b ) / 40 = 10 }}}
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(2) {{{ 16.5a + 9.25b = 400 }}}
(2) {{{ 1650a + 925b = 40000 }}}
(2) {{{ 66a + 37b = 1600 }}}
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Multiply both sides of (1) by {{{ 37 }}}
and subtract (1) from (2)
(2) {{{ 66a + 37b = 1600 }}}
(1) {{{ -37a - 37b = -1480 }}}
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{{{ 29a = 120 }}}
{{{ a = 4.138 }}}
and, since
(1) {{{ a + b = 40 }}}
(1) {{{ b = 35.862 }}}
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4.1 pounds of macadamias are needed
35.9 pounds of standard mix are needed
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check answer:
(2) {{{ ( 16.5a + 9.25b ) / 40 = 10 }}}
(2) {{{ ( 16.5*4.1 + 9.25*35.9 ) / 40 = 10 }}}
(2) {{{ ( 67.65 + 332.08 ) / 40 = 10 }}}
(2) {{{ 399.73 = 400 }}}
Error due to rounding off -I think
Hope this helps