Question 452445
Let {{{a}}} = liters of 25% juice needed
Let {{{b}}} = liters of 10% juice needed
given:
OJ in 25% juice: {{{ .25a }}}
OJ in 10% juice: {{{ .1b }}}
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(1) {{{ a + b = 15 }}}
(2) {{{ ( .25a + .1b ) / 15 = .13 }}}
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(2) {{{ .25a + .1b = 1.95 }}}
(2) {{{ 25a + 10b = 195 }}}
Multiply both sides of (1) by {{{ 10 }}} and
subtract (1) from (2)
(2) {{{ 25a + 10b = 195 }}}
(1) {{{ -10a - 10b = -150 }}}
{{{ 15a = 45 }}}
{{{ a = 3 }}}
and
(1) {{{ 3 + b = 15 }}}
{{{ b = 12 }}}
3 liters of 25% juice are needed
12 liters of 10% juice are needed
check:
(2) {{{ ( .25a + .1b ) / 15 = .13 }}}
(2) {{{ ( .25*3 + .1*12 ) / 15 = .13 }}}
(2) {{{ ( .75 + 1.2 ) / 15 = .13 }}}
(2) {{{ 1.95 / 15 = .13 }}}
(2) {{{ 1.95 = 1.95 }}}
OK