Question 418674
Let {{{a}}} = gallons of 11% solution needed
Let {{{b}}} = gallons of 7% solution needed
given:
(1) {{{a + b = 44}}}
{{{ ( .11a + .07b )/44 = .1 }}}
{{{.11a + .07b = 4.4 }}}
(2) {{{11a + 7b = 440 }}}
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Multiply both sides of (1) by {{{7}}}
and subtract (1) from (2)
(2) {{{11a + 7b = 440 }}}
(1) {{{-7a - 7b = -308 }}}
{{{4a = 132 }}}
{{{ a = 33 }}}
and, since
{{{ a + b = 44 }}}
{{{ b = 44 - 33 }}}
{{{b = 11}}}
33 gallons of 11% solution are needed
11 gallons of 7% solution are needed
check answer:
{{{ ( .11a + .07b )/44 = .1 }}}
{{{ ( .11*33 + .07*11 )/44 = .1 }}}
{{{ ( 3.63 + .77 ) / 44 = .1 }}}
{{{ 4.4 / 44 = .1 }}}
{{{4.4 = 4.4 }}}
OK