Question 288399: the sum of three numbers is 14.the sum of twice the first number,5 times the second number,and 6 times the third number is 72.the difference between 5 times the first number and the second number is 6.find the three numbers
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! the sum of three numbers is 14.
the sum of twice the first number, 5 times the second number, and 6 times the
third number is 72.
the difference between 5 times the first number and the second number is 6.
find the three numbers
;
Three numbers, x, y, z
:
Write an equation for each statement:
:
"the sum of three numbers is 14."
x + y + z = 14
:
"the sum of twice the first number, 5 times the second number,and 6 times the
third number is 72."
2x + 5y + 6z = 72
:
"the difference between 5 times the first number and the second number is 6."
5x - y = 6
y = (5x-6); use this for substitution
:
Add 5x - y to the 1st equation
x + y + z = 14
5x- y + 0 = 6
----------------- eliminates y
6x + z = 20
z = (20-6x); use this for substitution
:
Substitute in 2x + 5y + 6z = 72
2x + 5(5x-6) + 6(20-6x) = 72
2x + 25x- 30 + 120 - 36x = 72
2x + 25x - 36x - 30 + 120 = 72
-9x + 90 = 72
-9x = 72 - 90
-9x = -18
x = +2
:
I'll let you find y and z, check your solution in the 1st equation
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