Question 1147232
Let {{{ a }}} = pints of 45% juice needed
Let {{{ b }}} = pints of 95% juice needed
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(1) {{{ .45a + .95b = 160 }}}
(2) {{{ 160 / ( a + b ) = .8 }}}
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(1) {{{ 45a + 95b = 16000 }}}
(1) {{{ 9a + 19b = 3200 }}}
and
(2) {{{ .8a + .8b = 160 }}}
(2) {{{ 8a + 8b = 1600 }}}
(2) {{{ a + b = 200 }}}
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Multiply both sides of (2) by {{{ 9 }}}
and subtract (2) for (1)
(1) {{{ 9a + 19b = 3200 }}}
(2) {{{ -9a - 9b = -1800 }}}
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{{{ 10b = 1400 }}}
{{{ b = 140 }}}
and
(2) {{{ a + b = 200 }}}
(2) {{{ a + 140 = 200 }}}
(2) {{{ a = 60 }}}
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60 pints of 45% juice are needed
140 pints of 95% juice are needed
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check:
(1) {{{ .45a + .95b = 160 }}}
(1) {{{ .45*60 + .95*140 = 160 }}}
(1) {{{ 27 + 133 = 160 }}}
(1) {{{ 160 = 160 }}}
OK
get a 2nd opinion on this if needed