Question

Teresa has $451 in a personal bank account,and then withdraws $10 per week.Andrew has $10 in a personal bank account,and then deposits $53 earned from dog grooming each week.After how many weeks will they have the same amount of money in the bank.

Answer 1

Given:

Teresa has $451 in a personal bank account,and then withdraws $10 per week.

Andrew has $10 in a personal bank account,and then deposits $53 each week.

To find:

After how many weeks will they have the same amount of money in the bank.

Solution:

Let x be the number of weeks after which they have the same amount.

Teresa has $451 in a personal bank account,and then withdraws $10 per week. So, the amount in Teresa's account is:

$\text{Teresa's account}=451-10x$

Andrew has $10 in a personal bank account,and then deposits $53 each week. So, the amount in his account is:

$\text{Andrew's account}=10+53x$

They have equal amount after x weeks. So,

$451-10x=10+53x$

Isolate variable terms.

$451-10=10x+53x$

$441=63x$

Divide both sides by 63.

$\dfrac{441}{63}=x$

$7=x$

Therefore, they will have the same amount of money in the bank after 7 weeks.