Question 769326
Let {{{ a }}} = total grams of alloy A
Let {{{ b }}} = total grams of alloy B
(1) {{{ a + b = 15 + 9 }}}
(1) {{{ a + b = 24 }}}
(2) {{{ (3/4)*a + (1/4)*b = 15 }}}
(3) {{{ ( 1/4)*a + (3/4)*b = 9 }}}
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(2) {{{ 3a + b = 60 }}}
(3) {{{ a + 3b = 36 }}}
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Subtract (1) from (2) 
(2) {{{ 3a + b = 60 }}}
(1) {{{ -a - b = -24 }}}
{{{ 2a = 36 }}}
{{{ a = 18 }}}
and
(3) {{{ a + 3b = 36 }}}
(3) {{{ 18 + 3b = 36 }}}
(3) {{{ 3b = 18 }}}
(3) {{{ b = 6 }}}
Alloy A weighs 18 g
Alloy B weighs 6 g
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check:
(1) {{{ a + b = 24 }}}
(1) {{{ 18 + 6 = 24 }}}
(1) {{{ 24 = 24 }}}
OK