Question

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

to the number, the digits will be interchanged. Find the number.
Please make an equation and solve it.​

Answer 1

27

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

Answer 2

Answer: The number is 27

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

-9x + 9y = 45

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