If Alex gives Bob a penny, Bob will have three times as many pennies as Alex has. If Bob gives Alex a penny, Bob will have twice as many pennies as Alex has. How many pennies does Bob currently have?
Let $a$ be the number of pennies that Alex currently has, and let $b$ be the number of pennies that Bob currently has. If Alex gives Bob a penny, Alex will have $a - 1$ pennies and Bob will have $b + 1$ pennies. Also, Bob will have three times as many pennies as Alex has, so $b + 1 = 3(a - 1) = 3a - 3$. If Bob gives Alex a penny, Alex will have $a + 1$ pennies and Bob will have $b - 1$ pennies. Also, Bob will have twice as many pennies as Alex has, so $b - 1 = 2(a + 1) = 2a + 2$.

If we subtract the second equation from the first, we obtain $2 = a - 5$, so $a = 7$. Plugging this in, we can find that $b = 17$, so Bob has $\boxed{17}$ pennies.
17
Level 4
Algebra
Problem: If Alex gives Bob a penny, Bob will have three times as many pennies as Alex has. If Bob gives Alex a penny, Bob will have twice as many pennies as Alex has. How many pennies does Bob currently have?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>Let A represent the number of pennies Alex has, and B represent the number of pennies Bob has. 

From the first statement, if Alex gives Bob a penny, then Alex will have A - 1 pennies and Bob will have B + 1 pennies. The condition states that Bob will then have three times as many pennies as Alex:

B + 1 = 3(A - 1)

From the second statement, if Bob gives Alex a penny, then Alex will have A + 1 pennies and Bob will have B - 1 pennies. The condition states that Bob will then have twice as many pennies as Alex:

B - 1 = 2(A + 1)

Now we have a system of two equations:

1. B + 1 = 3(A - 1)
2. B - 1 = 2(A + 1)

We can simplify both equations. 

From the first equation:

B + 1 = 3A - 3
B = 3A - 4

From the second equation:

B - 1 = 2A + 2
B = 2A + 3

Now we have two expressions for B:

3A - 4 = 2A + 3

To solve for A, we subtract 2A from both sides:

3A - 2A - 4 = 3
A - 4 = 3

Adding 4 to both sides gives:

A = 7

Now we substitute A back into one of the equations to find B. Using B = 3A - 4:

B = 3(7) - 4
B = 21 - 4
B = 17

Thus, the number of pennies Bob currently has is 17.<|END_OF_LATENT|> The final answer is $17$.