Question 590208
Call the numbers {{{a}}}, {{{b}}}, and {{{c}}}
given:
(1) {{{ a + b + c = 63 }}}
(2) {{{ b = 5a + 3 }}}
(3) {{{ c = 2a - 4 }}}
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There are 3 equations and 3 unknowns, so it's solvable
Substitute (3) into (1)
(1) {{{ a + b + 2a - 4 = 63 }}}
(1) {{{ 3a + b = 67 }}}
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(2) {{{ 5a - b = -3 }}}
Add (1) and (2)
(2) {{{ 5a - b = -3 }}}
(1) {{{ 3a + b = 67 }}}
{{{ 8a = 64 }}}
{{{ a = 8 }}}
Plug this back into (3)
(3) {{{ c = 2*8 - 4 }}}
(3) {{{ c = 16 - 4 }}}
(3) {{{ c = 12 }}}
Plug this into (1)
(1) {{{ a + b + 12 = 63 }}}
(1) {{{ 8 + b + 12 = 63 }}}
(1) {{{ b = 63 - 20 }}}
(1) {{{ b = 43 }}}
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check:
(2) {{{ b = 5a + 3 }}}
(2) {{{ 43 = 5*8 + 3 }}}
(2) {{{ 43 = 43 }}}
OK