Question

3. A two-digit number is eight times the sum of its digits. If 45 is
subtracted from the numbers, the position of digits get interchanged.
Find the number.​

Answer 1

Step-by-step explanation:

If x is the tens place digit and y is the ones place digit, we can write the value of the number like this: 10x + y.

 

So the value of the number is 8 times the sum of its digits:

 

10x + y = 8(x + y)

 

How can we show that the number's digits are reversed using our variables? The number's digits being reversed means that the digit that was in the tens place is now in the ones place and vice versa. So the reversed digit number would look like this: 10y + x.  

 

(10x + y) - 45 = 10y + x

 

Now you can solve the system of equations.

 

10x + y = 8(x + y)              solve for one variable, in this case I'll choose x

2x = 7y

x = 7/2y, or 3.5y

 

(10x + y) - 45 = 10y + x                           go to your second equation

(10*3.5y + y) -45 = 10y + 3.5y                         plug in for x

36y - 45 = 13.5y

22.5y = 45

y = 2

 

x = 3.5y                             go back to the equation where you solved for x in terms of y

x = 3.5(2)                                    plug in for y

x = 7

 

The number is 72.

 

Let's check!

 

1. 72 = 8(7+2)

   72 = 8(9)

   72 = 72  

 

2. 72 - 45 = 27

   27 = 27