bob has $x$ dollars now. if pat gives bob a dollar, bob will have twice as many dollars as pat. of bob gave pat a dollar instead, they both will have the same number of dollars. what is the value of $x

Bob has $7 dollars now.

Explanation:

b = Bob's original amount of money ($x$ dollars)

p = Pat's original amount of money

"If Pat gives Bob a dollar, Bob will have twice as many dollars as Pat."

b + 1 = 2 (p-1)

b + 1 = 2p - 2

b = 2p - 2 - 1

b = 2p - 3

"If Bob g Pat a dollar instead, they both will have the same number of dollars."

p + 1 = b - 1

p = b - 1 - 1

p = b - 2

In the first equation replace p with (x-2)

b = 2 (b-2) - 3

b = 2b - 4 - 3

b = 2b - 7

7 = 2b - b

7 = b