You can
put this solution on YOUR website!Help needed please
Find X, Y, and Z
X + Y + Z = 1150
X = 4Z + 100
X = 6Y + 50
Solve the 2nd eq for Z:
X = 4Z + 100
X - 100 = 4Z
Divide every term by 4
-
=
-
=
=
-
Solve the 3rd eq for Y:
X = 6Y + 50
X - 50 = 6Y
Divide every term by 6
-
=
-
=
=
-
Substitute
=
-
and
=
-
into the first equation:
X + Y + Z = 1150
X + (
-
) + (
-
) = 1150
X +
-
+
-
= 1150
Nultiply every term by 12
12·X + 12·
- 12·
+ 12·
- 12·
= 12·1150
12X + 2X - 100 + 3X - 300 = 13800
17X - 400 = 13800
17X = 13800 + 400
17X = 14200
X =
Substitute X =
in X = 6Y + 50
X = 6Y + 50
= 6Y + 50
Multiply through by 17
17·
= 17·6Y + 17·50
14200 = 102Y + 850
14200 - 850 = 102Y
13350 = 102Y
= Y
That fraction reduces by dividing top and bottom
by 6:
= Y
800 - 50 = 6Y
750 = 6Y
125 = Y
Substitute X =
in X = 4Z + 100
X = 4Z + 100
= 4Z + 100
Multiply through by 17
17·
= 17·4Z + 17·100
14200 = 68Z + 1700
14200 - 1700 = 68Z
12500 = 68Z
= Z
That fraction reduces by dividing top and bottom
by 4:
= Z
So the solution is
(X, Y, Z) = (
,
,
)
Are you sure your teacher asked you to solve such a
horrible problem with such nasty fractions? This solution
is correct for what you gave me. But I'll bet anything that
there is a sign wrong somewhere in the original problem.
Edwin
