The sum of r and p is equal to twice s, and p is 36 less than twice the sum of r and s. What is the value of r ?
Correct Answer: 12
The phrase "the sum of r and p is equal to twice s" can be written as r + p = 2s. The phrase "p is 36 less than twice the sum of r and s" can be written as p = 2(r + s) - 36. From the first equation, p = 2s - r. Substituting this expression for p into the second equation yields
|2s - r||=||2(r + s) - 36|
|2s - r||=||2r + 2s - 36|
|-r||=||2r - 36|
The value of r is 12.
(from the October 12, 1999 test)