Solution: $5.  

If Timmy has $1, then Mara must have $3. But when her mother gives her $20, she will have a total of 3 + 20 = 23, which is more than seven times the amount that Timmy has. (In fact, it is 23 times as much as Timmy has.) A table can be used to investigate other amounts, and the table below shows that the conditions of the problem are satisfied if Timmy has $5.

It’s also possible to use algebra to solve this problem. Let x = Timmy’s amount. Then Mara currently has 3x dollars, and she will have 3x + 20 after her mother gives her $20. Since Mara’s new amount is supposed to be seven times Timmy’s current amount, this leads to the equation 3x + 20 = 7x. Solving this equation yields x = 5, which verifies the answer in the table.