A number of two digits is increased by 36 when the digits are reversed. the sum of the digits is 10. Find the number.

Expert Answers
mwestwood eNotes educator| Certified Educator

37 is the number you seek.  When this number is reversed, the number 73 is created; 37 + 36 = 73.  Thus 37 is increased by 36 when the digits are reversed.  And, the sum of           3 + 7= 10.

atyourservice | Student

The number is 37. 

37 + 36 = 73

7 + 3 =10

revolution | Student

let X be the number in units place and Y be the number in the tens place

The sum of the digits in a two-digit is 7 and can be expressed as:

X+Y=10- eqn 1

When the digits are reversed, it can be expressed as this:

10X+Y

But, you also kow that when the digits are reversed, a number of two digits is increwased by 36 so:

10X+Y=10Y+X+36- eqn 2

Using the first equation, make X as the subject, so:

X=10-Y- eqn 3

Sub eqn 3 to eqn 2:

10(10-Y)+Y=10Y+(10-Y)+36

100-10Y+Y=10Y+10-Y+36

100-9Y=9Y+46

18Y= 54

Y=3

Sub. Y=3 ino eqn 1

X+3=10

X=7

As X= number in units place and Y= number in tens place, so

the two digit number would be 37

Double-check for mistakes:

the sum of digits of 37= 3+7=10 (correct)

When digit is reversed, 73

Compare the two numbers: 73 and 37

The difference between the two numbers

= 73-37

= 36 (correct)

In all, 37 is the two-digit number.