Question 519443
Let {{{a}}} = pounds of $6 coffee needed
Let {{{b}}} = pounds of $4.50 coffee needed
given:
(1) {{{ a + b = 30 }}}
(2) {{{ (60a + 45b) / 30 = 53 }}} ( in dimes)
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(2) {{{ 60a + 45b = 1590 }}}
(2) {{{ 4a + 3b = 106 }}}
Multiply both sides of (1) by {{{3}}}
and subtract (1) from (2)
(2) {{{ 4a + 3b = 106 }}}
(1) {{{ -3a - 3b = -90 }}} 
{{{ a = 16 }}}
and, since
(1) {{{ a + b = 30 }}}
(1) {{{ b = 30 - 16 }}}
(1) {{{ b = 14 }}}
16 pounds of $6 coffee are needed
14 pounds of $4.50 coffee are needed
check:
(2) {{{ (60*16 + 45*14) / 30 = 53 }}}
(2) {{{ (960 + 630) / 30 = 53 }}}
(2) {{{ 1590 = 53*30 }}}
(2) {{{ 1590 = 1590 }}}
OK