Question 760543
Let {{{ a }}} = ounces of 13% ink needed
Let {{{ b }}} = ounces of 17% ink needed
{{{ .13a }}} = ounces of cobalt blue color in 13% ink
{{{ .17b }}} = ounces of cobalt blue color in 17% ink
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(1) {{{ a + b = 256 }}}
(2) {{{ ( .13a + .17b ) / 256 = .15 }}}
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(2) {{{ .13a + .17b = .15*256 }}}
(2) {{{ .13a + .17b = 38.4 }}}
(2) {{{ 13a + 17b = 3840 }}}
Multiply both sides of (1) by {{{ 13 }}}
and subtract (1) from (2)
(2) {{{ 13a + 17b = 3840 }}}
(1) {{{ -13a - 13b = -3328 }}}
{{{ 4b = 512 }}}
{{{ b = 128 }}}
and, since
(1) {{{ a + b = 256 }}}
(1) {{{ a + 128 = 256 }}}
(1) {{{ a = 128 }}}
128 ounces of 13% ink are needed
128 ounces of 17% ink are needed
check:
(2) {{{ ( .13*128 + .17*128 ) / 256 = .15 }}}
(2) {{{ ( 16.64 + 21.76 ) / 256 = .15 }}}
(2) {{{ 38.4 = .15*256 }}}
(2) {{{ 38.4 = 38.4 }}}
OK