Question 1179511

1.(a) Write an expression in terms of x and y for the total value of a two digit number having x as tens digits and y as the units digit.

10x+y

(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.

3(x+y)+8=10x+y
3x+3y +8 = 10x+y
7x-2y=8-----------------------(1)

When the digits are reversed the value of the number is increased by 9.Find the number.
10y+x 10x+y+9
9y-9x=9
y-x=1
y=(x+1)

Substitute y in (1)
7x-2y=8
7x-2(x+1)=8
7x-2x-2=8
5x=10
x=2

y-x =1

so y =3

The number is 23