Final answer:
If John has 15 dollars less than Abby. If John doubles his money, and Abby spends half of hers, then they will both have the same amount of money then Abby has $20 and John has $5. Option b is correct.
Step-by-step explanation:
Let's assume Abby has x dollars.
According to the given information, John has $15 less than Abby, so John has x - 15 dollars.
If John doubles his money, he will have 2(x - 15) dollars.
If Abby spends half of her money, she will have x/2 dollars left.
According to the problem, when John doubles his money and Abby spends half of hers, they will have the same amount of money. So, we can set up the equation:
2(x - 15) = x/2
Simplifying the equation:
2x - 30 = x/2
Multiplying both sides of the equation by 2 to eliminate the fraction:
4x - 60 = x
Subtracting x from both sides of the equation:
3x - 60 = 0
Adding 60 to both sides of the equation:
3x = 60
Dividing both sides of the equation by 3:
x = 20
So, Abby has 20 dollars and John has x - 15 = 20 - 15 = 5 dollars.
Therefore, the correct option is: b) John has $30, Abby has $45.