Question

Christiana and Marlena opened their first savings accounts on the same day. Christiana opened her account with $45 and plans to deposit $10 every month. Marlena opened her account with $35 and plans to deposit $15 every month. After how many months will their two accounts have the same amount of money? What will that amount be?

Answer 1

Answer: it will take 2 months for both accounts to have the same amount and the in each account would be $65

Explanation:

Let x represent the number of days that it will take the amount in either accounts to be the same.

Let y represent the amount in Christiana's account after x days

Let z represent the amount in Marlena's account after x days

Christiana opened her account with $45 and plans to deposit $10 every month. This means that in x days, the amount in Christiana's account would be

y = 45 + 10x

Marlena opened her account with $35 and plans to deposit $15 every month. This means that in x days, the amount in Marlena's account would be

z = 35 + 15x

To determine the number of months before the amount in both accounts becomes the same, we will equate y to z. It becomes

45 + 10x = 35 + 15x

15x - 10x = 45 - 35

5x = 10

x = 10/5 = 2

The amount would be

45 + 10×2 = 45 + 20 = $65

Answer 2

After 2 months their accounts have same amount of money that is $65.

Explanation:

Initial amount Christiana deposits = $45

Amount Christiana deposit each month = $10

Initial amount Marlena deposits = $35

Amount Marlena deposit each month = $15

Let x be the number of months after which amount in accounts is same.

Christiana balance in x months = 45 + 10x

Marlena balance in x months = 35 + 15x

After x months their balance becomes equal i.e.

45 + 10x = 35 + 15x

dividing both sides by 5

9 + 2x = 7 + 3x

x = 2

After two months:

Christiana balance = 45 + 10(2)

= $65

Marlena balance = 35 + 15(2)

= $65