Question 168385
There are 3 equations and 3 unknowns, so 
it should be solvable
(1) {{{x + y + z = 1150}}} given
(2) {{{x = 4z - 100}}} given
(3) {{{4z = x + 100}}}
(4) {{{z = (1/4)*x + 25}}}
(5) {{{x = 6y + 50}}} given
(6) {{{6y = x - 50}}}
(7) {{{y = (1/6)*x - 25/3}}}
Now substitute (4) and (7) into (1)
(8) {{{x + (1/6)*x - 25/3 + (1/4)*x + 25 = 1150}}}
Multiply both sides by {{{12}}}
(9) {{{12x + 2x - 100 + 3x + 300 = 13800}}}
(10) {{{17x = 13600}}}
{{{x = 800}}}
And from (4)
(4) {{{z = (1/4)*x + 25}}}
(11) {{{z = (1/4)*800 + 25}}}
(12) {{{z = 225}}}
And from (7)
(7) {{{y = (1/6)*x - 25/3}}}
(13) {{{y = (1/6)*800 - 25/3}}}
(14) {{{y = (2*800 - 4*25) / 12}}}
(15) {{{y = 1500/12}}}
(16) {{{y = 125}}}
The answers are x = 800, y = 125, z = 225
check answers:
(1) {{{x + y + z = 1150}}} given
(2) {{{x = 4z - 100}}} given
(5) {{{x = 6y + 50}}} given
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(1) {{{x + y + z = 1150}}}
(17) {{{800 + 125 + 225 = 1150}}}
(18) {{{1150 = 1150}}}
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(2) {{{x = 4z - 100}}}
(19) {{{800 = 4*225 - 100}}}
(20) {{{800 = 800}}}
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(5) {{{x = 6y + 50}}} given
(21) {{{800 = 6*125 + 50}}}
(22) {{{800 = 800}}}
OK