SOLUTION: The second of three numbers is twice the first. The third is 6 less than the second. If the second is decreased by 3 times the third, the result is 50. Find the numbers.

Question 504165: The second of three numbers is twice the first. The third is 6 less than the second. If the second is decreased by 3 times the third, the result is 50. Find the numbers.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Three numbers: x, y, z.
x is the first number
y is second
z is third
.
The second is twice the first.
y = 2x
.
Their third is 6 less than the second.
z = y-6
so
y = z+6
.
If the second is decreased by 3 times the third, the result is 50
y -3z = 50
y = 3z +50
.
Since y=y,
z+6 = 3z+50
-2z = 44
z = -22
.
y = z+6
y = -16
.
y = 2x
2x = -16
x = -8
.
check the solution.
.
Is the second number twice the first number?
-16 = 2*-8
correct.
.
If the second is decreased by 3 times z, is the result 50?
-16 -(3*-22) = -16 +66 = 50
correct.
.
Answer: The three integers are -8, -16, and -22.
.
Done.

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