Question

*A number consisting of two digits is three times the sum of its digits. If 45 is added

Answer 1

Answer: The number is 27

              The system of equations is:     7x - 2y = 0

                                                                 -9x + 9y = 45

Step-by-step explanation:

Let x represent the number in the tens place and y represent the number in the ones place.  x y

Then 10x + y = 3(x + y)

When the digits are reversed: 10y + x = 10x + y + 45

Simplify each of the above equations and then create a system of equations:

10x + y = 3x + 3y             →        7x - 2y  = 0

10y + x = 10x + y + 45      →       -9x + 9y = 45

9( 7x - 2y  =  0)    →      63x - 18y = 0

2(-9x + 9y = 45)   →     -18x + 18y = 90

                                     45x         = 90

                                                x  =  2  

Input x = 2 into either equation to solve for y:

7x - 2y  = 0

7(2) - 2y = 0

14          = 2y

          7 = y

Answer 2

Answer:

27

Step-by-step explanation:

Let's say that the number is 10x + y

Accordingly the number consists of digits three times the sum of it's digits, so 10x + y = 3(x + y)

10x + y = 3(x + y) -> Distribute the "3"

10x + y = 3x + 3y -> Combine like terms

7x = 2y -> Isolate "x"

x = 2y/7 --- (1)

With the information provided, the number (10x + y) when added to 45, equals the "interchanged" digits. In this case x and y represents digits, so interchanging them would be 10y + x;

10x + y + 45 = 10y + x -> Combine like terms

9x = 9y - 45 --- (2)

Substitute the first equation into the second, and solve for x and y. Given the digits we can determine the number =>

9(2y/7) = 9y - 45 -> Simplify

- 45y/7 = - 45 -> Multiply either side by 7

- 45y = - 315 -> Divide either side by - 45

y = - 315/ -45 = 7 (second digit)

x = 2(7)/7 = 14/7 = 2 (first digit)  

Solution: The number is 27