Malory isn’t putting money in two savings accounts. account a started with $150 and account b started with $300.malory deposits $16 in account a and $12 in account b each month. in how many months will account a have a balance at least as great as account b? what will that balance be?

Given:

To Find:

The number of months where the balance of both is equal and the balance itself.

Solution:

In 37.5 months, the account balances in both accounts will be equal.

This balance will be equal to $750 in both account A and B.

Calculation:

Let x be the number of months where both the accounts have equal balance.

So, at the end of x months, 16x is the amount of money that will be added to account A (since $16 is added every month).

And the total amount at the end of x months will therefore be $(150+16x)

Similarly, at the end of x months, 12x is the amount of money that will be added to account B (since $12 will be added every month).

And the total amount at the end of x months will therefore be $(300+12x)

By our assumption, x is the number of months it will take for both the accont balances will be equal. Therefore, we have the equation

Therefore, in 37.5 months, the account balances in both accounts will be equal.

This balance will be equal to i.e. $750 will be the balance in both account A and B.

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