Question 516819: Solve-A 2-digit no. Is such that the product of its digits is 18.When 63 is subtracted from the no. the digits interchange their position.Find the nos.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! With digit problems you have to look at a number in terms of the place values of its digits. Consider the number 'xy' which does NOT mean x*y, but rather x being next to y.
.
The value of 'xy' is 10x + y.
.
x*y = 18
so
x = 18/y
.
10x + y -63 = 10y + x
.
subsitute
.
10*18/y +y -63 = 10y +18/y
.
180/y + y -63 = 10y + 18/y
.
multiply through by y to eliminate the fractions
.
180 + y^2 -63y = 10y^2 + 18
.
collect terms
.
10y^ + 18 = y^2 -63y + 180
9y^2 +63y -162 = 0
.
divide by 9
.
y^2 +7y - 18 = 0
.
factor
.
(y+9)(y-2) = 0
.
y = -9 or 2
.
Substitute 2
.
x*2 = 18
x = 9
.
The original number appears to be: 92.
.
The product of 9*2 = 18, which is how the solution was found.
To check these values, you have to use the other equation.
.
92 - 63 = 29
Yep. The digits are interchanged.
.
Answer: The original number is 92. The other number is 29.
.
Done.
.
But what about the y=-9?
Well, it is not a single digit.
x*-9 = 18
x = -2
.
-29 -63 = -92
.
So in a sense it works, but we would need a means to show a negative number with a different symbol that takes only one space for this solution to make common sense.
|
|
|
