SOLUTION: I need help with the following problem. Someone spilled ink on a bill for 36 sweatshirts. If only the first and last digits were covered and the other three digits were, in ord

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Question 86742This question is from textbook Mathematics for elementary teachers
: I need help with the following problem.
Someone spilled ink on a bill for 36 sweatshirts. If only the first and last digits were covered and the other three digits were, in order, 8, 3, 9 as in
?83.9?, how much did each cost?
I do not have a clue how to do this problem. Please help.
Thank you for your time, it is appreciated.
Sincerely,
R. Franke
This question is from textbook Mathematics for elementary teachers

Found 2 solutions by Edwin McCravy, ankor@dixie-net.com:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
I need help with the following problem. 
Someone spilled ink on a bill for 36 sweatshirts. If only the first and last
digits were covered and the other three digits were, in order, 8, 3, 9 as in
?83.9?, how much did each cost? 
I do not have a clue how to do this problem. Please help.
Thank you for your time, it is appreciated.
Sincerely,
R. Franke

The price was $_83.9_ or _839_ in pennies. 

Let's find the smallest possible price in pennies one shirt could have
cost. 

The smallest way to fill in those blanks is with a 1 in the first blank
and a 0 in the last blank, or 18390. But 18390 is not a multiple of 36.
The smallest multiple of 36 above that is 18396. Therefore the smallest
possible price for the 36 shirts must be 18396 which is 36×511.

So, hey, that's the answer! 36 shirts for 511 cents each or $5.11 each.
Or at least it's AN answer.

If 36 shirts cost 18396 pennies, then that cost in dollars is

$183.96.

I'm not sure if that's THE ONLY answer but it IS indeed AN answer.
Each shirt cost $5.11 and the price of 36 of them is $183.96.

Edwin


Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Someone spilled ink on a bill for 36 sweatshirts. If only the first and last digits were covered and the other three digits were, in order, 8, 3, 9 as in
?83.9?, how much did each cost?
:
Here's another approach:
WE have: __ 8 3 . 9 __
:
We know the greatest cost of a shirt is 983.99/36 = $27.33 a shirt or less.
Probably above $15 a shirt
:
Using a Ti83 table and equation y = 36t, TblStart at 15, increment at .01
looked for value of y that satisfy the above.
:
Came up with a shirt cost of $16.22 * 36 = $583.92 as the value on the bill
: