Question 493024
Let {{{a}}} = pounds of 10% silver alloy to be added
Let {{{b}}} = pounds of 60% silver alloy to be added
given:
{{{ .1a }}} = pounds of silver in 10% alloy
{{{ .6b }}} = pounds of silver in 60% alloy
{{{ .4*10 = 4 }}} = pounds of silver in final alloy
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(1) {{{ a + b = 10 }}}
(2) {{{ .1a + .6b = 4 }}}
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(2) {{{ a + 6b = 40 }}}
Subtract (1) from (2)
(2) {{{ a + 6b = 40 }}}
(1) {{{ -a - b = -10 }}}
{{{ 5b = 30 }}}
{{{ b = 6 }}}
and, since
(1) {{{ a + b = 10 }}}
(1) {{{ a + 6 = 10 }}}
(1) {{{ a = 4 }}}
4 pounds of 10% silver alloy need to be added
6 pounds of 60% silver alloy need to be added
check answer:
(2) {{{ .1a + .6b = 4 }}}
(2) {{{ .1*4 + .6*6 = 4 }}}
(2) {{{ .4 + 3.6 = 4 }}}
(2) {{{ 4 = 4 }}}
OK