Question 758245
Let {{{ a }}} = pounds of 34% alloy needed
Let {{{ b }}} = pounds of 55% alloy needed
{{{ .34a }}} = pounds of copper in {{{ a }}}
{{{ .55b }}} = pounds of copper in {{{ b }}}
----------------------------------
given:
(1) {{{ a + b = 49 }}}
(2) {{{ ( .34a + .55b ) / 49 = .4 }}}
----------------------------
(2) {{{ .34a + .55b = .4*49 }}}
(2) {{{ .34a + .55b = 19.6 }}}
(2) {{{ 34a + 55b = 1960 }}}
Multiply both sides of (1) by {{{ 34 }}} and
subtract (1) from (2)
(2) {{{ 34a + 55b = 1960 }}}
(1) {{{ -34a - 34b = -1666 }}}
{{{ 21b = 294 }}}
{{{ b = 14 }}}
and, since
(1) {{{ a + b = 49 }}}
(1) {{{ a + 14 = 49 }}}
(1) {{{ a = 35 }}}
35 pounds of 34% alloy are needed
14 pounds of 55% alloy are needed
check:
(2) {{{ ( .34a + .55b ) / 49 = .4 }}}
(2) {{{ ( .34*35 + .55*14 ) / 49 = .4 }}}
(2) {{{  11.9 + 7.7 = .4*49 }}}
(2) {{{ 19.6 = 19.6 }}}
OK