Question

Alan and Judith begin withdrawing money from their accounts at the same time.

Alan has $10,350 in his account and withdraws $1,096 at the end of each month.
Judith has $8,400 in her account and withdraws $822 at the end of each month. If
they do not make any other deposits or withdrawals, at the end of which month will
Judith's account have more money than Alan's account?
A. 5th
B. 7th
C. 6th
D. 8th

Answer 1

Judith's account will have more money than Alan's account at the end of the 8th month.

Step-by-step explanation:

To find out at which month Judith's account will have more money than Alan's account, we need to compare their balances at the end of each month until Judith's account surpasses Alan's.

Alan's account balance after x months can be represented by the equation: 10,350 - 1,096x.

Judith's account balance after x months can be represented by the equation: 8,400 - 822x.

Setting the two equations equal to each other and solving for x, we have:

10,350 - 1,096x = 8,400 - 822x

Subtracting 8,400 from both sides gives:

1,950 - 1,096x = -822x

Combining like terms:

1,950 = 274x

Dividing both sides by 274:

x = 7.12

Since we can't have fractions of months, we round up to the next whole number, which is 8.

Therefore, Judith's account will have more money than Alan's account at the end of the 8th month.