SOLUTION: I need help on this word problem. The sum of three numbers is 18 the first is eight times the sum of the second and third. the sum of the first number and the last number is 11. fi

Question 435934: I need help on this word problem. The sum of three numbers is 18 the first is eight times the sum of the second and third. the sum of the first number and the last number is 11. find the numbers.
I put the first equation: x+y+z=18 and I also figured out the last one: x+z=11
but i cant figure out the second equation: The sum of three numbers is 18 the first is eight times the sum of the second and third. Can you please help me?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of three numbers is 18 the first is eight times the sum of the second and third.
the sum of the first number and the last number is 11. find the numbers.
:
The equation for,"the first is eight times the sum of the second and third."
x = 8(y+z)
which is
x = 8y + 8z
We can write it
x - 8y - 8z = 0
:
Multiply the 1st equation by 8, add to the above equation,
8x + 8y + 8z = 144
x - 8y - 8z = 0
---------------------addition eliminates y and z find x
9x = 144
x =
x = 16 is the 1st number
then
x + z = 11
16 + z = 11
z = 11 - 16
z = -5
and
x + y + z = 18
16 + y -5 = 18
y = 18 - 11
y = 7
:
The three numbers are: 16, -5, 7
:
:
Check solution in the statement:"the first is eight times the sum of the second and third."
16 = 8(7 - 5)
16 = 8(2)
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