Question 889122
Let {{{ a }}},  {{{ b }}}, {{{ c }}}, and {{{ d }}} be the numbers
(1) {{{ ( a + b + c + d ) / 4 = 56 }}}
(2) {{{ a = b + 5 }}}
(3) {{{ c = (1/2)*b }}}
(4) {{{ d = 3*( a + b ) }}}
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Substitute (2) into (4)
(4) {{{ d = 3*( b + 5 + b ) }}}
(4) {{{ d = 3*( 2b + 5 ) }}}
(4) {{{ d = 6b + 15 }}}
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Substitute (2), (3), and (4) into (1)
(1) {{{ ( a + b + c + d ) / 4 = 56 }}}
(1) {{{ ( b + 5 + b + (1/2)*b + 6b + 15 ) / 4 = 56 }}}
(1) {{{ ( ( 17/2 )*b + 20 ) / 4 = 56 }}}
Multiply both sides by {{{ 4 }}}
(1) {{{  ( 17/2 )*b + 20  = 224 }}}
Multiply both sides by {{{ 2 }}}
(1) {{{ 17b + 40 = 448 }}}
(1) {{{ 17b = 408 }}}
(1) {{{ b = 24 }}}
and
(2) {{{ a = b + 5 }}}
(2) {{{ a = 24 + 5 }}}
(2) {{{ a = 29 }}}
and
(3) {{{ c = (1/2)*24 }}}
(3) {{{ c = 12 }}}
and
(4) {{{ d = 6*24 + 15 }}}
(4) {{{ d = 144 + 15 }}}
(4) {{{ d = 159 }}}
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The numbers are 29, 24, 12, and 159
check:
(1) {{{ ( a + b + c + d ) / 4 = 56 }}}
(1) {{{ ( 29 + 24 + 12 + 159 ) / 4 = 56 }}}
(1) {{{ 224/4 = 56 }}}
(1) {{{ 224 = 224 }}}
OK