+1694 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_
+1023
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.
.
