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Question Number 112573 by Aina Samuel Temidayo last updated on 08/Sep/20

	Answered by Rasheed.Sindhi last updated on 08/Sep/20

	$L e t t w o n u m b e r s a r e 10 a + b &$ $10 c + d w i t h 10 a + b > 10 c + d$ $A f t e r w r i t t e n b e s i d e :$ $100 (10 a + b) + (10 c + d)$ $A b s o l u t e d i f f e r n c e$ $(10 a + b) - (10 c + d)$ $T h e e q u a t i o n w i l l b e$ $100 (10 a + b) + (10 c + d)$ $- {(10 a + b) - (10 c + d)} = 5481$ $T o d e t e r m i n e :$ $(10 a + b) + (10 c + d)$ $1000 a + 100 b + 10 c + d$ $- 10 a - b + 10 c + d = 5481$ $\Rightarrow 990 a + 99 b + 20 c + 2 d = 5481$ $\Rightarrow 99 (10 a + b) + 2 (10 c + d) = 5481$ $10 a + b = \frac{5481 - 2 (10 c + d)}{99}$ $(10 a + b) + (10 c + d)$ $= \frac{5481 - 2 (10 c + d)}{99} + 10 c + d$ $= \frac{5481 - 2 (10 c + d) + 990 c + 99 d}{99}$ $= \frac{5481 + 970 c + 97 d}{99}$ $[W e h a v e t o d e t e r m i n e s u c h v a l u e s$ $o f c & d t h a t \frac{5481 + 970 c + 97 d}{99} \in N]]$ $N o w,$ $1 ⩽ c ⩽ 9 \land 0 ⩽ d ⩽ 9 :$ $S o,$ $F o r c = 1 & d = 8 :$ $= \frac{5481 + 970 (1) + 97 (8)}{99} = 73$ $(T h e n u m b e r s a r e 55 & 18)$
	Commented by Rasheed.Sindhi last updated on 08/Sep/20

	$C o m p l e t e d .$
	Commented by Aina Samuel Temidayo last updated on 08/Sep/20

	$Please finish it .$
	Commented by Aina Samuel Temidayo last updated on 08/Sep/20

	$How does one solve for c and d ?$
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