Question 1089003
Let the numbers be a, b, and c
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(1) {{{ a + b + c = 11 }}}
(2) {{{ 2a + 4b + 5c = 30 }}}
(3) {{{ 6a - b = 47 }}}
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(3) {{{ b = 6a - 47 }}}
Plug this into (1)
(1) {{{ a + 6a - 47 + c = 11 }}}
(1) {{{ c = -7a + 58 }}}
Plug this into (2)
(2) {{{ 2a + 4b + 5*( -7a + 58 ) = 30 }}}
(2) {{{ 2a + 4b - 35a + 290 = 30 }}}
(2) {{{ 33a - 4b = 260 }}}
Multiply bth sides of (3) by {{{ 4 }}} and
subtract (3) from (2)
(2) {{{ 33a - 4b = 260 }}}
(3) {{{ -24a + 4b = -188 }}}
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{{{ 9a = 72 }}}
{{{ a = 8 }}}
and
(3) {{{ b = 6a - 47 }}}
(3) {{{ b = 6*8 - 47 }}} 
(3) {{{ b = 48 - 47 }}}
(3) {{{ b = 1 }}}
and
(1) {{{ a + b + c = 11 }}}
(1) {{{ 8 + 1 + c = 11 }}}
(1) {{{ c = 2 }}}
The numbers are 8, 1, and 2
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check:
(2) {{{ 2a + 4b + 5c = 30 }}}
(2) {{{ 2*8 + 4*1 + 5*2 = 30 }}}
(2) {{{ 16 + 4 + 10 = 30 }}}
(2) {{{ 30 = 30 }}}
OK
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You can check (3)