The units' digit of a two-digit number is 5 more than the tens' digit, and the number is three times as great as the sum of the digits. Find the number.

The number is 27

Step-by-step explanation:

Let the 10s digit be x

Let the units digit be y

y = x + 5

10x + y = 3 (x + y) Remove the brackets

10x + y = 3x + 3y Substitute the x + 5 into the second equation for y

10x + x + 5 = 3x + 3 (x + 5) Remove the brackets on the right.

10x + x + 5 = 3x + 3x + 15 Collect like terms on each side.

11x + 5 = 6x + 15 Subtract 5 from both sides

11x + 5 - 5 = 6x + 15 - 5 Collect like terms

11x = 6x + 10 Subtract 6x from both sides

11x - 6x = 6x - 6x + 10

5x = 10 Divide by 5

5x/5 = 10/5

x = 2

y = x + 5

y = 2 + 5

y = 7