Edy has $450 in her savings account. She deposits $40 each month. Juan has $975 in his checking account. He writes a check for $45.45 each month for his cell phone bill and $19.55... Edy has $450 in her savings account. She deposits $40 each month. Juan has $975 in his checking account. He writes a check for $45.45 each month for his cell phone bill and $19.55 each month for his water bill. After how many months will Edy and Juan have the same amount of money in their accounts? Read more

Steps to Solve

1. Identify Initial Balances and Monthly Changes

   Edy's initial balance is $450. She deposits $40 each month. This means her balance after $x$ months can be expressed as: $$ E = 450 + 40x $$

   Juan's initial balance is $975. He writes checks for a total of $45.45 + $19.55 = $65 each month. His balance after $x$ months is given by: $$ J = 975 - 65x $$

2. Set Up the Equation for Balance Equality

   To find when their balances are equal, set the two equations from step 1 equal to each other: $$ 450 + 40x = 975 - 65x $$

3. Combine Like Terms

   Add $65x$ to both sides to eliminate $x$ from the right side: $$ 450 + 40x + 65x = 975 $$ $$ 450 + 105x = 975 $$

4. Isolate the Variable

   Subtract $450$ from both sides: $$ 105x = 975 - 450 $$ $$ 105x = 525 $$

5. Solve for $x$

   Divide both sides by 105 to solve for $x$: $$ x = \frac{525}{105} $$ $$ x = 5 $$