Question 1030286
Let {{{ a }}} = number of tables refinished using method 1
Let {{{ b }}} = number of tables refinished using method 2
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(1) {{{ .5a + 1.5b = 92 }}}
(2) {{{ 8a + 5b = 484 }}}
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(1) {{{ 5a + 15b = 920 }}}
(1) {{{ a + 3b = 184 }}}
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Multiply both sides of (1) by {{{ 8 }}}
and subtract (2) from (1)
(1) {{{ 8a + 24b = 1472 }}}
(2) {{{ -8a - 5b = -484 }}}
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{{{ 19b = 988 }}}
{{{ b = 52 }}}
and
(1) {{{ a + 3b = 184 }}}
(1) {{{ a + 3*52 = 184 }}}
(1) {{{ a + 156 = 184 }}}
(1) {{{ a = 28 }}}
They should refinish 28 tables using method 1
They should refinish 52 tables using method 2
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(1) {{{ .5a + 1.5b = 92 }}}
(1) {{{ .5*28 + 1.5*52 = 92 }}}
(1) {{{ 14 + 78 = 92 }}}
(1) {{{ 92 = 92 }}}
OK 
You can check (2)