Each of x, y, z, and u is a
positive integer that satisfies this set of equations:
- x + y = 3(z+u)
- x + z = 4(y+u)
- x + u = 5(y+z)
Determine the minimum value of x+y+z+u
The minimum sum is 120
x y z u sum
83 7 13 17 120
166 14 26 34 240
Adding all 3 equations yields:
3x = 8y + 7z + 6u
Subtracting various pairs of equations yields:
u = 4z - 5y
z = 2u - 3y
y = 5u - 6z
But I was not able to come up with an analytic full solution.
-------------
for y in range(1,200):
for z in range(1,big):
u = 4*z - 5*y
x = (8*y + 7*z + 6*u)/3
if x%1 == 0:
x = int(x)
if x + y != 3*(z+u):
continue
if x + z != 4*(y+u):
continue
if x + u != 5*(y+z):
continue
print(x,y,z,u, x+y+z+u)
Program Output:
83 7 13 17 120
166 14 26 34 240
249 21 39 51 360
332 28 52 68 480
415 35 65 85 600
498 42 78 102 720
etc
|
|
Posted by Larry
on 2023-09-29 07:19:25 |
computer solution
