Question

a two digit number becomes 18 more than another two digit number which is formed by interchanging the places of original number the number is

Answer 1

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Answer 2

What is the solution for the word problem: “A two digit number is such that the product of the digits is 8. When 18 is subtracted from the number, the digits are interchanged. Find the number?”?

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9 ANSWERS



Bibhu Prasad Mahananda

Answered Apr 23, 2018 · Author has 86answers and 5.1k answer views

Let the digits of the number be x(tens place) and y(ones place) .

So the number shall be10x+y10x+y. (This is because the algebraic notation of a number is the position of the digit times the digit. E.g; 11 is a number that can be written as 10*1 + 1.)

According to the question,

The product of the digits is 8. So,

xy=8xy=8

Or, y=8/xy=8/x…(1) (dividing ‘x’ both sides)

And when 18 is subtracted from the number the digits get interchanged;

So, (10x+y)−18=(10y+x)(10x+y)−18=(10y+x),

(this is because if the digits would be interchanged, then the digit of the ones place shall become the digit of the tens place and vice-versa. Thus 10x+y when interchanged becomes 10y+x.)

Or,10x+y−18=10y+x10x+y−18=10y+x (opening the brackets.)

Or, 10x−x−18=10y−y10x−x−18=10y−y (subtracting x and y both sides)

Or, 9x−18=9y9x−18=9y

Or, 9x−9y=189x−9y=18 (adding 18 and subtracting 9y on both sides)

Or, 9(x−y)=189(x−y)=18 (taking 9 common on the LHS)

Or, x−y=18/9x−y=18/9 (dividing 9 on both sides)

Or, x−y=2x−y=2

Or, x−(8/x)=2x−(8/x)=2 (from equation 1)

Or, x2−2x−8=0x2−2x−8=0 (On solving further)

Or, x2−4x+2x−8=0x2−4x+2x−8=0 (splitting the middle term)

Or, x(x−4)+2(x−4)=0x(x−4)+2(x−4)=0 (taking x common of the first two terms and 2 of the third and fourth terms respectively)

Or, (x−4)(x+2)=0(x−4)(x+2)=0 (Taking x-4 common)

Or,x=4|x=−2x=4|x=−2 (solving the problem with the zero product rule)

As, a digit cannot be negative, so we reject the value - 2 and take 4 as the value of x.

Substituting the value of ‘x’ in equation 1, we get :

y=8/4y=8/4

Or, y = 2

Thus the number (10x+y) is :

(10×4)+2=40+2=42(10×4)+2=40+2=42

Thus, the number is 42.


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