SOLUTION: The sum of three numbers is 180. The third is four times the first and the second is 36 less than the third. Let x, y, z be the first, second, and third number respectfully. Set u

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The sum of three numbers is 180. The third is four times the first and the second is 36 less than the third. Let x, y, z be the first, second, and third number respectfully. Set u      Log On


   



Question 1048533: The sum of three numbers is 180. The third is four times the first and the second is 36 less than the third. Let x, y, z be the first, second, and third number respectfully. Set up the system of linear equations to find the numbers.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
x%2B+y%2B+z=180........eq.1
The third is four times the first:z=4x........eq.2
the second is 36 less than the third:y=z-36........eq.3

x%2B+y%2B+z=180........eq.1......substitute z and y from eq.2 and eq.3
x%2B%28z-36%29%2B+4x=180.....substitute z from eq.2
x%2B4x-36%2B+4x=180....solve for x
9x=180%2B36
9x=144
highlight%28x=16%29
now, go to eq.2
z=4x........eq.2...substitute x and solve for z
z=4%2A16
highlight%28z=64%29
and, go to
y=z-36........eq.3.....substitute z and solve for y

y=64-36
highlight%28y=28%29