Question 517417
Let {{{a}}} = ounces of 11% alloy needed
Let {{{b}}} = ounces of 24% alloy needed
given:
(1) {{{ a + b = 130 }}}
(2) {{{ ( .11a + .24b ) / 130 = .16 }}}
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(2) {{{ .11a + .24b = .16*130 }}}
(2) {{{ .11a + .24b = 20.8 }}}
(2) {{{ 11a + 24b = 2080 }}}
Multiply both sides of (1) by {{{ 11 }}}
and subtract (1) from (2)
(2) {{{ 11a + 24b = 2080 }}}
(1) {{{ -11a - 11b = -1430 }}}
{{{ 13b = 650 }}}
{{{ b = 50 }}}
and, since
(1) {{{ a + b = 130 }}}
(1) {{{ a = 130 - 50 }}}
(1) {{{ a = 80 }}}
80 ounces of 11% alloy are needed
50 ounces of 24% alloy are needed
check:
(2) {{{ ( .11*80 + .24*50 ) / 130 = .16 }}}
(2) {{{ ( 8.8 + 12 ) / 130 = .16 }}}
(2) {{{ 20.8 = .16*130 }}}
(2) {{{ 20.8 = 20.8 }}}
OK