the units digit of a two-digit numeral is 5 more than the tens digit. the number is 3 times the sum of its digits. find the numeral.
To find the two-digit numeral, we'll let the tens digit be represented by 'x' and the units digit be 'y'.
According to the given information:
1) The units digit is 5 more than the tens digit ⇒ y = x + 5
2) The number is 3 times the sum of its digits ⇒ 10x + y = 3(x + y)
To solve for the two-digit numeral, we'll substitute the value of 'y' from equation (1) into equation (2):
10x + (x + 5) = 3(x + (x + 5))
Simplifying the equation:
10x + x + 5 = 3(2x + 5)
11x + 5 = 6x + 15
11x - 6x = 15 - 5
5x = 10
Dividing both sides of the equation by 5:
x = 2
Substituting the value of 'x' back into equation (1) to find 'y':
y = x + 5
y = 2 + 5
y = 7
So the tens digit is 2 and the unit digit is 7. Therefore, the numeral is 27.