Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Five times the sum of the digits of a two-digit number is 13 less than the original number. If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number. (Hint: You can use variables to represent the digits of a number. If a two-digit number has the digit x in tens place and y in one’s place, the number will be 10x + y. Reversing the order of the digits will change their place value and the reversed number will 10y + x.) The difference of the original two-digit number and the number with reversed digits is .

Answer 1

The difference of the original two-digit number and the number with reversed digits is 98 - 89 = 9

Explanation:

Let the digit at unit(one's) place = y

Let the digit at ten's place = x

So, the two-digit number will be: 10x +y

According to given condition:

Five times the sum of the digits of a two-digit number is 13 less than the original number. This statement can be written as:

5(x +y) = (10x +y) - 13

If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.

if digits are reserved the two digit will be 10y + x

4(x + y) = (10y + x) -21

So, we have 2 equations, solving these 2 equations we can find the 2 digit number.

5(x +y) = (10x +y) - 13

5x + 5y = 10x +y -13

Rearranging:

5x -10x +5y -y = -13

-5x + 4y = -13 (eq1)

4(x + y) = (10y + x) -21

4x +4y = 10y +x =-21

4x -x +4y -10y = -21

3x -6y = -21 (eq2)

Solving:

Multiply eq 1 with 3 and eq 2 with 2

-15x + 12 y = -39

6x - 12y = -42

_______________

-9x = -81

x = -81/-9

x = 9

Putting in eq(1)

-5x + 4y = -13

-5(9) +4y = -13

-45 + 4y = -13

4y = -13 + 45

4y = 32

y = 32/4

y = 8

So, y =8 and x = 9

The 2 digit number is:

10x + y = 10(9) + 8 = 90+8 = 98

The reversed 2 digit number is:

10y + x = 10(8) + 9 = 80+9 = 89

The difference of the original two-digit number and the number with reversed digits is 98 - 89 = 9