Question 716949
Let {{{ a }}} = liters of pure antifreeze to be used
Let {{{ b }}} = liters of 29.4% solution to be used
{{{ .294b }}} = liters of pure antifreeze in 29.4% solution
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given:
(1) {{{ a + b = 6.6 }}}
(2) {{{ ( a + .294b ) / 6.6 = .576 }}}
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(2) {{{ a + .294b = .576*6.6 }}}
(2) {{{ a + .294b = 3.8016 }}}
(2) {{{ 1000a + 294b = 3802 }}}
Multiply both sides of (1) by {{{ 294 }}} and
subtract (1) from (2)
(2) {{{ 1000a + 294b = 3802 }}}
(1) {{{ -294a - 294b = -1940 }}}
{{{ 706a = 1862 }}}
{{{ a = 2.6374 }}}
and, since
(1) {{{ 2.6374 + b = 6.6 }}}
(1) {{{ b = 3.9626 }}}
2.6374 liters of pure antifreeze must be used
check answer:
(2) {{{ ( 2.6374 + .294*3.9626 ) / 6.6 = .576 }}}
(2) {{{ ( 2.6374 + 1.1650 ) / 6.6 = .576 }}}
(2) {{{ 3.8024 / 6.6 = .576 }}}
(2) {{{ 3.8024 = 3.8016 }}}
OK- I think error is due to rounding off