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Write an expression in terms of x and y for the total value of a two digit number

(a) Write an expression in terms of x and y for the total value of a two digit number having x as the tens digit and y as the the units digit.
(b) The number in (a) above is such that three times the sum of its digits is less than the value of the number by 8. When the digits are reversed the value of the number increases by 9. Find the number.

Answers

(a) The total value of a two digit number is 10x + y

(b) Let the number be xy

3(x + y) =(10 + y) + 8

3x + 3y = 10x + y + 8

7x - 2y = 8

The reversed number is yx

Therefore 10y + x - 10x - y = 9

9y -9x = 9

9(7x -2y = 8)

2(-9x + 9y= 9)

63x - 18y = 72

-18x + 18y = 18

45x = 90

x = 2

7x - 2y = 8

14 - 2y = 8

2y = 6

y = 3

The number is 23

raphael answered the question on January 24, 2017 at 05:13

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