Fractions, Decimals, & Percents - Third Edition Typo?

by **rocketrules** Mon Nov 24, 2008 4:02 am

pg. 22
The example for the Unknown Digit Problem:
AB*CA = DEBC

What if A = 2, B= 4, C = 5
The product of these numbers would be 1248
So the B's are aligned.
Where am I screwing up?

by **JonathanSchneider** Sun Dec 07, 2008 12:14 pm

You're right that the B's would be aligned, but be careful! You've only satisfied one part of the solution (the tens place). Notice that under your scheme, the ones digit of the final product would be an 8, but this is NOT equal to your value for C.

In general, it's easiest to start with the ones digit on these problems.

by **Guest** Sat Dec 20, 2008 6:06 am

A= 4
B= 2
C= 8

In our parameters we have that C= AB, and B = (A)(A) + (B)(C)

It took me about 3-4 min. plugging in numbers to see what works

42
84
----
1428

Is there a shortcut, I'm sure there must be a more efficient way?

by **JonathanSchneider** Thu Dec 25, 2008 8:44 pm

I think I follow what you mean, but notice that the math you've written out isn't strictly correct. Instead, you have shown how we arrive at the digit that is in each of those places, not accounting for any carryover from the other places. For example, if the ones digits multiplied together from the first two integers to create some product more than 9, there would be a carryover into the tens place. This would then effect your digit there.

There is no direct shortcut for these problems, but you do need to start with the units digit and work up from there. You will often be told something else about the numbers as well, such as "They are all unique" or "ab < 10." This will help you to make the first step.