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?

Let's set up the equation based on the information given.

• Julio initially has $210 and saves $35 per month. After \( x \) months, his total amount will be: \[ 210 + 35x \]

• Alice initially has $300 and saves $20 per month. After \( x \) months, her total amount will be: \[ 300 + 20x \]

We want to find out when their amounts will be equal, so we set up the equation: \[ 210 + 35x = 300 + 20x \]

Now we can solve for \( x \). First, let's move all terms involving \( x \) to one side of the equation and constant terms to the other side: \[ 35x - 20x = 300 - 210 \] \[ 15x = 90 \]

Now divide both sides by 15: \[ x = 6 \]

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

To verify:

• After 6 months:
  • Julio: \( 210 + 35 \times 6 = 210 + 210 = 420 \)
  • Alice: \( 300 + 20 \times 6 = 300 + 120 = 420 \)

Both will indeed have $420 after 6 months, confirming that the solution is correct.