In a three-digit number, the hundred’s and ten’s digit are the same. The unit’s digit is 3 more than the hundred’s digit. If the number is reversed, the new number is 72 more than twice the original number. How do you find the number?

1 Answer
Apr 18, 2016

Answer:

So you can write the number as #aab# where #b=a+3#

Explanation:

This means that the value of the original number is:
#=100a+10a+(a+3)=111a+3#

The reversed number will be #baa#, or:
#=100(a+3)+10a+a=111a+300#

Twice the original number plus 72 equals the new number:
#2(111a+3)+72=111a+300->#
#222a+78=111a+300->#

Subtract #111a# and #78# from both sides:
#111a=222->a=2->b=a+3=5->#

The original number is #225#

Check your answer:
#2xx225+72=522#, check!