Question 815076
Let {{{ a }}} = pounds of type A coffee needed
Let {{{ b }}} = pounds of type B coffee needed
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(1) {{{ a + b = 156 }}}
(2) {{{ 4.2a + 5.3b = 756.4 }}}
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(2) {{{ 42a + 53b = 7564 }}}
Multiply both sides of (1) by {{{ 42 }}}
and subtract (1) from (2)
(2) {{{ 42a + 53b = 7564 }}}
(1) {{{ -42a - 42b = -6552 }}}
{{{ 11b = 1012 }}}
{{{ b = 92 }}}
and, since
(1) {{{ a + b = 156 }}}
(1) {{{ a + 92 = 156 }}} 
(1) {{{ a = 64 }}}
He used 92 pounds of type B coffee
check:
(2) {{{ 4.2*64 + 5.3*92 = 756.4 }}}
(2) {{{ 268.8 + 487.6 = 756.4}}}
(2) {{{ 756.4 = 756.4 }}}
OK