A school orders $99$ textbooks, all for the same price. When the bill for the total order comes, the first and last digits are obscured. What are the missing digits?

$_5801.3_

bIueb3rry Sep 4, 2024

#1**0 **

*A school orders $99$ textbooks, all for the same price. *

*When the bill for the total order comes, the first and last *

*digits are obscured. What are the missing digits? $_5801.3_ *

Consider that the price per book is multiplied by 99.

And, multiplying by 99 incorporates multiplying by 9.

The digits of the product of a number multiplied by 9

will always sum to a total that is evenly divisible by 9.

5 + 8 + 0 + 1 + 3 = 17 so the sum of the two missing

numbers will have to add 1 or 10 or 19, etc. to that 17.

Using brute force, I reckoned that 15801**.**39 is evenly

divided by 99. So the missing numbers are **1 and 9**.

And the cost of each textbook was 159**.**61.

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Bosco Sep 4, 2024