# the sum of digits of a two-digit number is 12. the value of the number is two more than 11 times the tens digit. find the number.please help me with this..

1
by kayeblancia

2014-11-13T22:36:28+08:00
Let 'x' be the number on the tens place
'y' be the number on the units place
'x(10)+y' be the number
----------------------------------------------------
From the statement 'the sum of a two-digit number is 12'
x + y = 12   ----equation 1
----------------------------------------------------
From the statement 'the value of the number is two more than 11 times the tens digit'
x(10) + y = 11x + 2
10x + y = 11x + 2
11x - 10x = y - 2
x = y -2       -----equation 2
----------------------------------------------------
Substitute equation 2 to equation 1
x + y = 12
y - 2 + y = 12
y+ y = 12 + 2
2y = 14
y = 7
----------------------------------------------------
Substitute y=7 to equation 1
x + y = 12
x + 7 = 12
x = 12 - 7
x = 5
---------------------------------------------------
The number as stated above is x(10) + y
10x + y = 10(5) + 7
= 50 + 7
= 57
---------------------------------------------------
Therefore the number is 57.