Question

A two digit number is 2 more than 5 times the sum of its digits. If the digit in the tens place is 1 less than the digit in the units place, find the number

Answer 1

Answer:

67

Step-by-step explanation:

let x be in the ten's place and y be in the unit's place

and the number be 10x + y

According to 1st condition,

10x + y = 2 + 5 ( x + y )

10x + y = 2 + 5x + 5y

10x - 5x + y - 5y = 2

5x - 4y = 2 _( 1st equation)

According to 2nd condition,

x = y -1

x - y = -1 _(2nd equation)

Multiplying equation 2 by 4,

4x - 4y = -4 _ ( 3rd equation)

Now , Subtracting equation 3 from 1

5x - 4y = 2

- 4x - 4y = -4

- + +

x = 6

therefore, x = 6.

place x = 6 in equation 2

therefore, 6 - y = -1

- y = -1 -6

- y = -7

therefore, y = 7

Now, placing the values of x and y in the number

therefore, 10(6) + 7

= 60 + 7

= 67

Ans : The number is 67