Question

I don't get this at all :(, here's the problem:
3AB + 2BA = B99
If A and B represent distinct digits correctly worked in the addition problem above, what is the value of A?

Answer 1

You know from the 10 and 1 place that A + B = 9. And from the 100 place you have
3 + 2 = B, i.e., B = 5.

Hence A = ...?

Answer 2

um..i still do't get it o:

Answer 3

3ab + 2ba = 99b
3a + 2a = 99
5a = 99
a = 99/5

Answer 4

Haha I think I've misunderstood the question ENTIRELY.

Answer 5

What we can do is look at each place: the units, the tens and the hundreds, and each of them gives us an equation.

LHS
= left-hand side
= 3AB + 2BA
= (3 * 100 + A * 10 + B * 1) + (2*100 + B*10 + A*1)
= (2+3)*100 + (A+B)*10 + (B+A)*1
= 5*100 + (A+B)*10 + (B+A)*1

So far so good?

Answer 6

I really have no idea D: where is the 399 from? Is this answer 153?

Answer 7

RHS = B99
= B*100 + 9*10 + 9*1

Yes?

Answer 8

right-hand side, is B99, not 399, and B99 is equal to
B99 = B*100 + 9*10 + 9*1
yes?

Answer 9

Hence the LHS = RHS if

5*100 + (A+B)*10 + (B+A)*1 = B*100 + 9*10 + 9*1

Yes?

Answer 10

I'm extremely lost, james D:

Answer 11

JAMES I NEED UR HELP BADLY

Answer 12

PLZ COME AFTER THIS

Answer 13

Ok. What does 123 mean?

123 = 1*100 + 2*10 + 3*1

do you agree?

Answer 14

Since 3AB + 2AB = B99, we can deduce that B has to be 5. The limit of 3AB is 399, the limit of 2BA is 299 - the sum of which is 698, therefore it cannot be 6 as we know it ends in 99. So B = 5.
From there, since 3+2 = 5, we can say that AB + BA = 99. Therefore find two two-digits numbers arranged in such a way that one is the reverse of the other, B represents 5 and they sum to 99 - 45, and 54 are the only matching pair.

Therefore A = 4.

Answer 15

but when you plug in those values, it doesn't work?

Answer 16

it does work. B = 5, A = 4 works:

599 = 345 + 254

Answer 17

OHHH they represent DIGITS IN the number. I was multiplying them.... /fail

Answer 18

Sorry JamesJ I didn't mean to steal your thunder, you were doing an excellent job explaining it.

Answer 19

no problem

Answer 20

CAN U HLP ME JAMES?

Answer 21

I left you a note on your problem.