Anumber consisting of two digits exceeds 4 times the sum of the digits by 3 .if 27 is added to the number, the place of the digits of the number are interchanged, find the number.

  47

Step-by-step explanation:

We can take x to represent the 10s digit and y the ones digit. Then we have ...

  (10x +y) - 4(x+y) = 3. . . . . a number exceeds 4 times the digit sum by 3

  (10x +y) +27 = (10y +x) . . . . . adding 27 swaps the digits

Simplifying these equations to standard form gives ...

  2x - y = 1

  x - y = -3

Subtracting the second equation from the first gives ...

  x = 4

  y = 2x -1 = 7

The number is 47.

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal