Question

Find all 3-digit numbers abc (bar on top) with the property that if this number is added to the number obtained by reversing the digits, the sum is 625. ( abc - bar on top- has the digit a in the hundreds place, b in the tens place, and c in the ones place.)

Answer 1

\[100a+10b+c+100c+10b+a=625\]

Answer 2

how would i solve that?

Answer 3

no idea

Answer 4

one equation, three variables so infinity many solutions, but they have to be positive integers between 1 and 9 so hmmmm

Answer 5

we could try some stuff

Answer 6

yes please!

Answer 7

well we could try a = 2, c = 3 so they add up to 5

Answer 8

then we would have
\[200+300+20b+5=625\] and solve for \(b\)

Answer 9

\[505+20b=625\\
20b=120

b=6\]

Answer 10

just grind it till you find it

Answer 11

typo there

Answer 12

Ahh that works i guess

a=1, c=4
a=2, c=3
a=3, c=2
a=4, c=1

work as well

Answer 13

yeah you get the same equation for each one
\[505+20b=625\]

Answer 14

abc : 100a + 10b + c
cba : 100c + 10b + a
====================
101(a+c) + 20b = 25*25

no matter what the value of b, 20b always ends up with 0
so a+c needs to be 5 or 15 for the last digit to be 5 on left hand side

Answer 15

thank you so much!