Word Problem

[DD2005]

Any help would be great!!

When you switch the digits you the same result. Why is this?
For Example:
21 x 24 = 504
12 x 42 = 504
or
84 x 36 = 3024
48 x 63 = 3024

 

[ting]

32 * 15 = 480


23 * 51 = 1173

Well that didn't work.

If the ratios equate it will work.

(21/12) = (42/24)

(84/48) = (63/36)

What relationship is the same in both your examples? How many examples can you find and what, if anything, do they all have in common?

 

[DD2005]

26x31= 806 or 62x13=806
a1=2
b1=6
a2=3
b2=1

a1 x a2 = 6
b1 x b2= 6

The examples in the 1st post come out equal as they do above.
21x24=504 or 12x42=504
a1xa2=4
b1xb2=4

Do the numbers in each problem have to equal each other for this to work out?

 

[Denis]

(10a + b)(10c +d) = (10b +a)(10d +c)
that'll end up with: ac = bd

Works with 3digit numbers also:
12 4 * 5 15 = 63860 ; 12*5 = 4*15
4 12 * 15 5 = 63860

 

[DD2005]

12 4 * 5 15 = 63860 ; 12*5 = 4*15
4 12 * 15 5 = 63860

Why does this work?