Question 522918
Let {{{a}}} = pounds of $9 coffee needed
Let {{{b}}} = pounds of $8 coffee needed
given:
(1) {{{ a + b = 20 }}}
(2) {{{ (9a + 8b) / 20 = 8.4 }}}
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(2) {{{ (9a + 8b) / 20 = 8.4 }}}
(2) {{{ 9a + 8b = 20*8.4 }}}
(2) {{{ 9a + 8b = 168 }}}
Multiply both sides of (1) by {{{8}}} and
subtract (1) from (2)
(2) {{{ 9a + 8b = 168 }}}
(1) {{{ -8a - 8b = 160 }}}
{{{ a = 8 }}}
and, since
(1) {{{ a + b = 20 }}}
(1) {{{ 8 + b = 20 }}}
(1) {{{ b = 12 }}}
8 pounds of $9 coffee are needed
12 pounds of $8 coffee are needed
check:
(2) {{{ (9a + 8b) / 20 = 8.4 }}}
(2) {{{ (9*8 + 8*12) / 20 = 8.4 }}}
(2) {{{ (72 + 96) = 8.4*20 }}}
(2) {{{ 168 = 168 }}}
OK