Question 617635
Let {{{ a }}} = the cost of a bar of soap
Let {{{ b }}} = the cost of a sponge
given:
(1) {{{ 2a + 6b = 5.5 }}}
(2) {{{ 3a + 5b = 8.25 }}}
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Multiply both sides of (1) by {{{3}}}
Multiply both sides of (2) by {{{2}}}
Then subtract (2) from (1)
(1) {{{ 6a + 18b = 16.5 }}}
(2) {{{ -6a - 10b = -16.5 }}}
{{{ 8b = 0 }}}
{{{ b = 0 }}}
and
(1) {{{ 2a = 5.5 }}}
(1) {{{ a = 2.75 }}}
and
(2) {{{ 3a = 8.25 }}}
(2) {{{ a = 2.75 }}}
It looks like the bars of soap are $2.75 each
and the sponges are free.