Math Word Problem

Question

Suppose that you made three purchases using your credit card during the month of January.

1.   The first purchase was on January 8^th for $457 .
2.  The second purchase was on January 19^th for $280.
3.  The third purchase was on January 24^th.

If your average daily balance for January was $695, what was the dollar amount of your last purchase? 

Remember:

1. There are 31 days in January.
2. You made no purchases between January 1st and January 7th.
3. This question is not asking for the card's final January balance. 

Round your answer to the nearest dollar. 

Answer 1

To find average daily balance you total the balance for everyday and divide by the number of days in that cycle. The easiest way to do this is enter the data in an excel sheet and write the daily balance for each day in January. Then you can sum all the numbers easily.

I'm going to do it shorthand by hand just to show you since the balance doesn't change much. The first seven days the balance is $0, then there's a purchase on the 19th and the balance is $457 for 12 days, next there's a purchase on the 24th and the balance is $457 + $280 = $737 for 5 days, then the last seven days the balance is $737 + x, an unknown number. We can use this information and the fact that the average daily balance is $695 to write an algebraic expression and solve for the dollar amount of the last purchase (x):

(7 * 0 + 12 * 457 + 5 * (737) + 7 * (737 + x)) / 31 = 695

(5,484 + 3685 + 5159 + 7x) / 31 = 695

14028 + 7x = 21545

7x = 7517

x = 1,073

The dollar amount for the last purchase was $1,073.00.