SOLUTION: Two consecutive numbers are represented by x and x + 1 if 6 is added to the first number and 2 is subtracted from the second number, the quotient of the new number is 9/2. determin

Question 1200952: Two consecutive numbers are represented by x and x + 1 if 6 is added to the first number and 2 is subtracted from the second number, the quotient of the new number is 9/2. determine the numbers algebraically.

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.
Two consecutive numbers are represented by x and x + 1 if 6 is added to the first number
and 2 is subtracted from the second number, the quotient of the new number is 9/2.
determine the numbers algebraically.
~~~~~~~~~~~~~~~~~~

First number becomes (x+6). Second number becomes ((x+1)-2) = (x-1). The ratio of the two new numbers is . This ratio equals : = . To solve this equation, cross multiply 2(x+6) = 9*(x-1). Simplify and find x 2x + 12 = 9x - 9 12 + 9 = 9x - 2x 21 = 7x x = 21/7 = 3, ANSWER. The two original numbers are 3 and 4.

Solved algebraically.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The original two numbers are x and x+1.

After adding 6 to the first number and subtracting 2 from the second, the two numbers are x+6 and x-1.

We are told that the quotient (ratio) of the two new numbers is 9/2:

The response from the other tutor shows how to solve that equation using formal algebra.

Informally, the equation can be solved quickly by observing that the difference between (x+6) and (x-1) is 7, and the difference between 9 and 2 is 7.

That means x+6 = 9 and x-1 = 2; both of those equations tell us that x = 3.

ANSWER: The original two numbers are x = 3 and x+1 = 4

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