Julio and Alice are saving money for their summer trip. Julio has $210 and saves $35 per month, Alice has $300 and saves only $20 per month. How many months will it take for them to have the same amount of money?

To determine how many months it will take for Julio and Alice to have the same amount of money, we can set up equations based on their current savings and their monthly savings.

Let's define \( x \) as the number of months.

The amount of money Julio will have after \( x \) months is given by: \[ \text{Julio's money} = 210 + 35x \]

The amount of money Alice will have after \( x \) months is given by: \[ \text{Alice's money} = 300 + 20x \]

We want to find when both amounts are equal: \[ 210 + 35x = 300 + 20x \]

To solve this equation, we can first isolate \( x \) by moving the terms involving \( x \) to one side and constant terms to the other side: \[ 210 + 35x - 20x = 300 \] \[ 210 + 15x = 300 \]

Next, we isolate \( 15x \) by subtracting 210 from both sides: \[ 15x = 300 - 210 \] \[ 15x = 90 \]

Now, we solve for \( x \) by dividing both sides by 15: \[ x = \frac{90}{15} \] \[ x = 6 \]

Therefore, it will take them 6 months for Julio and Alice to have the same amount of money.