A first number added to double the second number is 2. The difference of the first number and 3 times the second number is 27. Find the two numbers.
A) 0 and 1
B) 5 and
C) 12 and

Question

A first number added to double the second number is 2. The difference of the first number and 3 times the second number is 27. Find the two numbers.
A) 0 and 1 
B) 5 and 
C) 12 and

Quizplus · Accepted Answer

Let's call the first number "x" and the second number "y".
From the first sentence, we can set up the equation:
x + 2y = 2      (equation 1)
From the second sentence, we can set up the equation:
x - 3y = 27    (equation 2)
We can solve for x in equation 2:
x = 3y + 27
We can substitute this expression for x into equation 1:
(3y + 27) + 2y = 2
Simplifying the equation, we get:
5y = - 25
Therefore, y = -5
To find x, we can use either equation 1 or 2:
x + 2(-5) = 2 or x - 3(-5) = 27
x = 12
So the two numbers are 12 and -5. 
Therefore, the best choice is C.

A First Number Added to Double the Second Number Is